diff --git a/narwhals/_expression_parsing.py b/narwhals/_expression_parsing.py
index 148259d8f0..a7a28dad7f 100644
--- a/narwhals/_expression_parsing.py
+++ b/narwhals/_expression_parsing.py
@@ -29,7 +29,7 @@
     from narwhals.expr import Expr
     from narwhals.typing import CompliantDataFrame
     from narwhals.typing import CompliantExpr
-    from narwhals.typing import CompliantFrameT_contra
+    from narwhals.typing import CompliantFrameT
     from narwhals.typing import CompliantLazyFrame
     from narwhals.typing import CompliantNamespace
     from narwhals.typing import CompliantSeries
@@ -51,8 +51,8 @@ def is_expr(obj: Any) -> TypeIs[Expr]:
 
 
 def evaluate_into_expr(
-    df: CompliantFrameT_contra,
-    expr: CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co],
+    df: CompliantFrameT,
+    expr: CompliantExpr[CompliantFrameT, CompliantSeriesT_co],
 ) -> Sequence[CompliantSeriesT_co]:
     """Return list of raw columns.
 
@@ -72,9 +72,9 @@ def evaluate_into_expr(
 
 
 def evaluate_into_exprs(
-    df: CompliantFrameT_contra,
+    df: CompliantFrameT,
     /,
-    *exprs: CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co],
+    *exprs: CompliantExpr[CompliantFrameT, CompliantSeriesT_co],
 ) -> list[CompliantSeriesT_co]:
     """Evaluate each expr into Series."""
     return [
@@ -86,8 +86,8 @@ def evaluate_into_exprs(
 
 @overload
 def maybe_evaluate_expr(
-    df: CompliantFrameT_contra,
-    expr: CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co],
+    df: CompliantFrameT,
+    expr: CompliantExpr[CompliantFrameT, CompliantSeriesT_co],
 ) -> CompliantSeriesT_co: ...
 
 
@@ -257,15 +257,15 @@ def is_simple_aggregation(expr: CompliantExpr[Any, Any]) -> bool:
 
 
 def combine_evaluate_output_names(
-    *exprs: CompliantExpr[CompliantFrameT_contra, Any],
-) -> Callable[[CompliantFrameT_contra], Sequence[str]]:
+    *exprs: CompliantExpr[CompliantFrameT, Any],
+) -> Callable[[CompliantFrameT], Sequence[str]]:
     # Follow left-hand-rule for naming. E.g. `nw.sum_horizontal(expr1, expr2)` takes the
     # first name of `expr1`.
     if not is_compliant_expr(exprs[0]):  # pragma: no cover
         msg = f"Safety assertion failed, expected expression, got: {type(exprs[0])}. Please report a bug."
         raise AssertionError(msg)
 
-    def evaluate_output_names(df: CompliantFrameT_contra) -> Sequence[str]:
+    def evaluate_output_names(df: CompliantFrameT) -> Sequence[str]:
         return exprs[0]._evaluate_output_names(df)[:1]
 
     return evaluate_output_names
@@ -286,11 +286,11 @@ def alias_output_names(names: Sequence[str]) -> Sequence[str]:
 
 
 def extract_compliant(
-    plx: CompliantNamespace[CompliantFrameT_contra, CompliantSeriesT_co],
+    plx: CompliantNamespace[CompliantFrameT, CompliantSeriesT_co],
     other: Any,
     *,
     str_as_lit: bool,
-) -> CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co] | object:
+) -> CompliantExpr[CompliantFrameT, CompliantSeriesT_co] | object:
     if is_expr(other):
         return other._to_compliant_expr(plx)
     if isinstance(other, str) and not str_as_lit:
diff --git a/narwhals/_protocols.py b/narwhals/_protocols.py
new file mode 100644
index 0000000000..d796b589dc
--- /dev/null
+++ b/narwhals/_protocols.py
@@ -0,0 +1,312 @@
+"""Refinements/extensions on `Compliant*` protocols.
+
+Mentioned in https://github.com/narwhals-dev/narwhals/issues/2044#issuecomment-2668381264
+
+Notes:
+- `Reuse*` are shared `pyarrow` & `pandas`
+- No strong feelings on the name, borrowed from `reuse_series_(namespace_?)implementation`
+- https://github.com/narwhals-dev/narwhals/blob/70220169458599013a06fbf3024effcb860d62ed/narwhals/_expression_parsing.py#L112
+"""
+
+from __future__ import annotations
+
+from itertools import chain
+from operator import methodcaller
+from typing import TYPE_CHECKING
+from typing import Any
+from typing import Callable
+from typing import Protocol
+from typing import Sequence
+from typing import TypeVar
+
+from narwhals._expression_parsing import evaluate_output_names_and_aliases
+from narwhals.typing import CompliantDataFrame
+from narwhals.typing import CompliantExpr
+from narwhals.typing import CompliantNamespace
+from narwhals.typing import CompliantSeries
+
+if TYPE_CHECKING:
+    from types import ModuleType
+    from typing import Iterable
+    from typing import Iterator
+
+    from typing_extensions import Self
+    from typing_extensions import TypeIs
+
+    from narwhals.dtypes import DType
+    from narwhals.typing import NativeSeries
+    from narwhals.typing import _1DArray
+    from narwhals.utils import Implementation
+    from narwhals.utils import Version
+
+    T = TypeVar("T")
+
+NativeSeriesT_co = TypeVar("NativeSeriesT_co", bound="NativeSeries", covariant=True)
+ReuseSeriesT = TypeVar("ReuseSeriesT", bound="ReuseSeries[Any]")
+
+ReuseDataFrameT = TypeVar("ReuseDataFrameT", bound="ReuseDataFrame[Any]")
+
+
+class ReuseDataFrame(CompliantDataFrame, Protocol[ReuseSeriesT]):
+    def _evaluate_into_expr(
+        self: ReuseDataFrameT, expr: ReuseExpr[ReuseDataFrameT, ReuseSeriesT], /
+    ) -> Sequence[ReuseSeriesT]:
+        _, aliases = evaluate_output_names_and_aliases(expr, self, [])
+        result = expr(self)
+        if list(aliases) != [s.name for s in result]:
+            msg = f"Safety assertion failed, expected {aliases}, got {result}"
+            raise AssertionError(msg)
+        return result
+
+    def _evaluate_into_exprs(
+        self, *exprs: ReuseExpr[Self, ReuseSeriesT]
+    ) -> Sequence[ReuseSeriesT]:
+        return list(chain.from_iterable(self._evaluate_into_expr(expr) for expr in exprs))
+
+    # NOTE: `mypy` is **very** fragile here in what is permitted
+    # DON'T CHANGE UNLESS IT SOLVES ANOTHER ISSUE
+    def _maybe_evaluate_expr(
+        self, expr: ReuseExpr[ReuseDataFrame[ReuseSeriesT], ReuseSeriesT] | T, /
+    ) -> ReuseSeriesT | T:
+        if is_reuse_expr(expr):
+            result: Sequence[ReuseSeriesT] = expr(self)
+            if len(result) > 1:
+                msg = (
+                    "Multi-output expressions (e.g. `nw.all()` or `nw.col('a', 'b')`) "
+                    "are not supported in this context"
+                )
+                raise ValueError(msg)
+            return result[0]
+        return expr
+
+
+# NOTE: DON'T CHANGE THIS EITHER
+def is_reuse_expr(
+    obj: ReuseExpr[Any, ReuseSeriesT] | Any,
+) -> TypeIs[ReuseExpr[Any, ReuseSeriesT]]:
+    return hasattr(obj, "__narwhals_expr__")
+
+
+class ReuseExpr(
+    CompliantExpr[ReuseDataFrameT, ReuseSeriesT],
+    Protocol[ReuseDataFrameT, ReuseSeriesT],
+):
+    _call: Callable[[ReuseDataFrameT], Sequence[ReuseSeriesT]]
+    _depth: int
+    _function_name: str
+    _evaluate_output_names: Any
+    _alias_output_names: Any
+    _implementation: Implementation
+    _backend_version: tuple[int, ...]
+    _version: Version
+    _kwargs: dict[str, Any]
+
+    def __init__(
+        self: Self,
+        call: Callable[[ReuseDataFrameT], Sequence[ReuseSeriesT]],
+        *,
+        depth: int,
+        function_name: str,
+        evaluate_output_names: Callable[[ReuseDataFrameT], Sequence[str]],
+        alias_output_names: Callable[[Sequence[str]], Sequence[str]] | None,
+        implementation: Implementation,
+        backend_version: tuple[int, ...],
+        version: Version,
+        kwargs: dict[str, Any],
+    ) -> None: ...
+
+    def __call__(self, df: ReuseDataFrameT) -> Sequence[ReuseSeriesT]:
+        return self._call(df)
+
+    def __narwhals_namespace__(self) -> ReuseNamespace[ReuseDataFrameT, ReuseSeriesT]: ...
+
+    def _reuse_series_implementation(
+        self: ReuseExpr[ReuseDataFrameT, ReuseSeriesT],
+        attr: str,
+        *,
+        returns_scalar: bool = False,
+        **expressifiable_args: Any,
+    ) -> ReuseExpr[ReuseDataFrameT, ReuseSeriesT]:
+        from narwhals._expression_parsing import evaluate_output_names_and_aliases
+
+        plx = self.__narwhals_namespace__()
+        from_scalar = plx._create_series_from_scalar
+
+        # NOTE: Ideally this would be implemented differently for `pandas` and `pyarrow`
+        # - It wouldn't make sense to check the implementation for each call
+        # - Just copying over from the function
+        def func(df: ReuseDataFrameT, /) -> Sequence[ReuseSeriesT]:
+            _kwargs = {
+                arg_name: df._maybe_evaluate_expr(arg_value)
+                for arg_name, arg_value in expressifiable_args.items()
+            }
+            # For PyArrow.Series, we return Python Scalars (like Polars does) instead of PyArrow Scalars.
+            # However, when working with expressions, we keep everything PyArrow-native.
+            extra_kwargs = (
+                {"_return_py_scalar": False}
+                if returns_scalar and self._implementation.is_pyarrow()
+                else {}
+            )
+            method = methodcaller(attr, **extra_kwargs, **_kwargs)
+            out: Sequence[ReuseSeriesT] = [
+                from_scalar(method(series), reference_series=series)
+                if returns_scalar
+                else method(series)
+                for series in self(df)
+            ]
+            _, aliases = evaluate_output_names_and_aliases(self, df, [])
+            if [s.name for s in out] != list(aliases):  # pragma: no cover
+                msg = (
+                    f"Safety assertion failed, please report a bug to https://github.com/narwhals-dev/narwhals/issues\n"
+                    f"Expression aliases: {aliases}\n"
+                    f"Series names: {[s.name for s in out]}"
+                )
+                raise AssertionError(msg)
+            return out
+
+        return plx._create_expr_from_callable(
+            func,
+            depth=self._depth + 1,
+            function_name=f"{self._function_name}->{attr}",
+            evaluate_output_names=self._evaluate_output_names,
+            alias_output_names=self._alias_output_names,
+            kwargs={**self._kwargs, **expressifiable_args},
+        )
+
+    def _reuse_series_namespace_implementation(
+        self: ReuseExpr[ReuseDataFrameT, ReuseSeriesT],
+        series_namespace: str,
+        attr: str,
+        **kwargs: Any,
+    ) -> ReuseExpr[ReuseDataFrameT, ReuseSeriesT]:
+        plx = self.__narwhals_namespace__()
+        return plx._create_expr_from_callable(
+            lambda df: [
+                getattr(getattr(series, series_namespace), attr)(**kwargs)
+                for series in self(df)
+            ],
+            depth=self._depth + 1,
+            function_name=f"{self._function_name}->{series_namespace}.{attr}",
+            evaluate_output_names=self._evaluate_output_names,
+            alias_output_names=self._alias_output_names,
+            kwargs={**self._kwargs, **kwargs},
+        )
+
+
+class ReuseSeries(CompliantSeries, Protocol[NativeSeriesT_co]):  # type: ignore[misc]
+    _name: str
+    _native_series: NativeSeriesT_co
+    _implementation: Implementation
+    _backend_version: tuple[int, ...]
+    _version: Version
+
+    def __init__(
+        self,
+        native_series: NativeSeriesT_co,
+        *,
+        implementation: Implementation,
+        backend_version: tuple[int, ...],
+        version: Version,
+    ) -> None: ...
+
+    def __array__(self: Self, dtype: Any, copy: bool | None) -> _1DArray: ...
+    def __contains__(self: Self, other: Any) -> bool: ...
+    def __iter__(self: Self) -> Iterator[Any]: ...
+    def __len__(self: Self) -> int:
+        return len(self._native_series)
+
+    def __narwhals_series__(self: Self) -> Self:
+        return self
+
+    # NOTE: Each side adds an `AssertionError` guard first
+    # Would probably make more sense to require a ClassVar, either:
+    # - defining the set of permitted impls
+    # - setting an unbound method, which also gives the error message
+    #   - E.g. `PandasLikeSeries._ensure = Implementation.ensure_pandas_like`
+    #   - That gets called w/ `ReuseSeries._ensure(ReuseSeries._implementation)`
+    def __native_namespace__(self: Self) -> ModuleType:
+        return self._implementation.to_native_namespace()
+
+    @classmethod
+    def _from_iterable(
+        cls: type[Self],
+        data: Iterable[Any],
+        name: str,
+        *,
+        implementation: Implementation,
+        backend_version: tuple[int, ...],
+        version: Version,
+    ) -> Self: ...
+    def _from_native_series(self: Self, series: NativeSeriesT_co | Any) -> Self: ...
+    @property
+    def dtype(self: Self) -> DType: ...
+    @property
+    def name(self: Self) -> str:
+        return self._name
+
+
+class ReuseNamespace(
+    CompliantNamespace[ReuseDataFrameT, ReuseSeriesT],
+    Protocol[ReuseDataFrameT, ReuseSeriesT],
+):
+    _implementation: Implementation
+    _backend_version: tuple[int, ...]
+    _version: Version
+
+    def __init__(
+        self,
+        implementation: Implementation,
+        backend_version: tuple[int, ...],
+        version: Version,
+    ) -> None: ...
+
+    def __narwhals_expr__(
+        self,
+    ) -> Callable[..., ReuseExpr[ReuseDataFrameT, ReuseSeriesT]]: ...
+    # Both do very similar things:
+    # - `_pandas_like.utils.create_compliant_series`
+    # - `_arrow.series.ArrowSeries(native_series=pa.chunked_array([value]))`
+    def _create_compliant_series(self, value: Any) -> ReuseSeriesT: ...
+
+    # NOTE: Fully spec'd
+    def _create_expr_from_callable(
+        self,
+        func: Callable[[ReuseDataFrameT], Sequence[ReuseSeriesT]],
+        *,
+        depth: int,
+        function_name: str,
+        evaluate_output_names: Callable[[ReuseDataFrameT], Sequence[str]],
+        alias_output_names: Callable[[Sequence[str]], Sequence[str]] | None,
+        kwargs: dict[str, Any],
+    ) -> ReuseExpr[ReuseDataFrameT, ReuseSeriesT]:
+        return self.__narwhals_expr__()(
+            func,
+            depth=depth,
+            function_name=function_name,
+            evaluate_output_names=evaluate_output_names,
+            alias_output_names=alias_output_names,
+            implementation=self._implementation,
+            backend_version=self._backend_version,
+            version=self._version,
+            kwargs=kwargs,
+        )
+
+    # NOTE: Fully spec'd
+    def _create_expr_from_series(
+        self, series: ReuseSeriesT
+    ) -> ReuseExpr[ReuseDataFrameT, ReuseSeriesT]:
+        return self.__narwhals_expr__()(
+            lambda _df: [series],
+            depth=0,
+            function_name="series",
+            evaluate_output_names=lambda _df: [series.name],
+            alias_output_names=None,
+            implementation=self._implementation,
+            backend_version=self._backend_version,
+            version=self._version,
+            kwargs={},
+        )
+
+    def _create_series_from_scalar(
+        self, value: Any, *, reference_series: ReuseSeriesT
+    ) -> ReuseSeriesT: ...
diff --git a/narwhals/typing.py b/narwhals/typing.py
index f1b62179e6..3d1a55aa07 100644
--- a/narwhals/typing.py
+++ b/narwhals/typing.py
@@ -3,7 +3,6 @@
 from typing import TYPE_CHECKING
 from typing import Any
 from typing import Callable
-from typing import Generic
 from typing import Literal
 from typing import Protocol
 from typing import Sequence
@@ -74,30 +73,28 @@ def aggregate(self, *exprs: Any) -> Self:
         # (so, no broadcasting is necessary).
 
 
-CompliantFrameT_contra = TypeVar(
-    "CompliantFrameT_contra",
-    bound="CompliantDataFrame | CompliantLazyFrame",
-    contravariant=True,
+CompliantFrameT = TypeVar(
+    "CompliantFrameT", bound="CompliantDataFrame | CompliantLazyFrame"
 )
 CompliantSeriesT_co = TypeVar(
     "CompliantSeriesT_co", bound=CompliantSeries, covariant=True
 )
 
 
-class CompliantExpr(Protocol, Generic[CompliantFrameT_contra, CompliantSeriesT_co]):
+class CompliantExpr(Protocol[CompliantFrameT, CompliantSeriesT_co]):
     _implementation: Implementation
     _backend_version: tuple[int, ...]
     _version: Version
-    _evaluate_output_names: Callable[[CompliantFrameT_contra], Sequence[str]]
+    _evaluate_output_names: Callable[[CompliantFrameT], Sequence[str]]
     _alias_output_names: Callable[[Sequence[str]], Sequence[str]] | None
     _depth: int
     _function_name: str
 
-    def __call__(self, df: Any) -> Sequence[CompliantSeriesT_co]: ...
+    def __call__(self, df: CompliantFrameT) -> Sequence[CompliantSeriesT_co]: ...
     def __narwhals_expr__(self) -> None: ...
     def __narwhals_namespace__(
         self,
-    ) -> CompliantNamespace[CompliantFrameT_contra, CompliantSeriesT_co]: ...
+    ) -> CompliantNamespace[CompliantFrameT, CompliantSeriesT_co]: ...
     def is_null(self) -> Self: ...
     def alias(self, name: str) -> Self: ...
     def cast(self, dtype: DType) -> Self: ...
@@ -119,13 +116,13 @@ def broadcast(
     ) -> Self: ...
 
 
-class CompliantNamespace(Protocol, Generic[CompliantFrameT_contra, CompliantSeriesT_co]):
+class CompliantNamespace(Protocol[CompliantFrameT, CompliantSeriesT_co]):
     def col(
         self, *column_names: str
-    ) -> CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co]: ...
+    ) -> CompliantExpr[CompliantFrameT, CompliantSeriesT_co]: ...
     def lit(
         self, value: Any, dtype: DType | None
-    ) -> CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co]: ...
+    ) -> CompliantExpr[CompliantFrameT, CompliantSeriesT_co]: ...
 
 
 class SupportsNativeNamespace(Protocol):
@@ -325,7 +322,7 @@ class DTypes:
     # This one needs to be in TYPE_CHECKING to pass on 3.9,
     # and can only be defined after CompliantExpr has been defined
     IntoCompliantExpr: TypeAlias = (
-        CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co] | CompliantSeriesT_co
+        CompliantExpr[CompliantFrameT, CompliantSeriesT_co] | CompliantSeriesT_co
     )
 
 
diff --git a/narwhals/utils.py b/narwhals/utils.py
index 0babd5440a..f628ed6f03 100644
--- a/narwhals/utils.py
+++ b/narwhals/utils.py
@@ -53,7 +53,7 @@
     from narwhals.series import Series
     from narwhals.typing import CompliantDataFrame
     from narwhals.typing import CompliantExpr
-    from narwhals.typing import CompliantFrameT_contra
+    from narwhals.typing import CompliantFrameT
     from narwhals.typing import CompliantLazyFrame
     from narwhals.typing import CompliantSeries
     from narwhals.typing import CompliantSeriesT_co
@@ -411,6 +411,20 @@ def is_ibis(self: Self) -> bool:
         """
         return self is Implementation.IBIS  # pragma: no cover
 
+    def ensure_pandas_like(self: Self) -> None:
+        if self.is_pandas_like():
+            return
+        pandas_like = {Implementation.PANDAS, Implementation.CUDF, Implementation.MODIN}
+        msg = f"Expected pandas-like implementation ({pandas_like}), found {self}"
+        raise TypeError(msg)
+
+    # NOTE: Not sure why this differs from `pandas_like`
+    def ensure_pyarrow(self: Self) -> None:
+        if self.is_pyarrow():
+            return
+        msg = f"Expected pyarrow, got: {type(self)}"  # pragma: no cover
+        raise AssertionError(msg)
+
 
 MIN_VERSIONS: dict[Implementation, tuple[int, ...]] = {
     Implementation.PANDAS: (0, 25, 3),
@@ -1321,8 +1335,8 @@ def is_compliant_series(obj: Any) -> TypeIs[CompliantSeries]:
 
 
 def is_compliant_expr(
-    obj: CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co] | Any,
-) -> TypeIs[CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co]]:
+    obj: CompliantExpr[CompliantFrameT, CompliantSeriesT_co] | Any,
+) -> TypeIs[CompliantExpr[CompliantFrameT, CompliantSeriesT_co]]:
     return hasattr(obj, "__narwhals_expr__")
 
 
diff --git a/pyproject.toml b/pyproject.toml
index dd4244f426..23418264bf 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -247,6 +247,7 @@ ignore_missing_imports = true
 [[tool.mypy.overrides]]
 module = [
   "*._expression_parsing",
+  "*._protocols",
   "*.utils",
   "*._pandas_like.*",
   "*._ibis.*",