diff --git a/narwhals/_dispatch.py b/narwhals/_dispatch.py
new file mode 100644
index 0000000000..b07702ce61
--- /dev/null
+++ b/narwhals/_dispatch.py
@@ -0,0 +1,83 @@
+from __future__ import annotations
+
+from collections.abc import Callable
+from functools import partial
+from typing import TYPE_CHECKING, Any, Generic, Protocol, TypeVar, overload
+
+if TYPE_CHECKING:
+
+    class Deferred(Protocol):
+        def __call__(self, f: Callable[..., R], /) -> JustDispatch[R]: ...
+
+
+__all__ = ["just_dispatch"]
+
+R = TypeVar("R")
+R_co = TypeVar("R_co", covariant=True)
+PassthroughFn = TypeVar("PassthroughFn", bound=Callable[..., Any])
+"""Original function is passed-through unchanged."""
+
+
+class JustDispatch(Generic[R_co]):
+    """Single-dispatch wrapper produced by decorating a function with `@just_dispatch`."""
+
+    __slots__ = ("_registry", "_upper_bound")
+
+    def __init__(self, function: Callable[..., R_co], /, upper_bound: type[Any]) -> None:
+        self._upper_bound: type[Any] = upper_bound
+        self._registry: dict[type[Any], Callable[..., R_co]] = {upper_bound: function}
+
+    def dispatch(self, tp: type[Any], /) -> Callable[..., R_co]:
+        """Get the implementation for a given type."""
+        if f := self._registry.get(tp):
+            return f
+        if issubclass(tp, self._upper_bound):
+            f = self._registry[tp] = self._registry[self._upper_bound]
+            return f
+        msg = f"{self._registry[self._upper_bound].__name__!r} does not support {tp.__name__!r}"
+        raise TypeError(msg)
+
+    def register(
+        self, tp: type[Any], *tps: type[Any]
+    ) -> Callable[[PassthroughFn], PassthroughFn]:
+        """Register types to dispatch via the decorated function."""
+
+        def decorate(f: PassthroughFn, /) -> PassthroughFn:
+            self._registry.update((tp_, f) for tp_ in (tp, *tps))
+            return f
+
+        return decorate
+
+    def __call__(self, arg: object, *args: Any, **kwds: Any) -> R_co:
+        """Dispatch on the type of the first argument, passing through all arguments."""
+        return self.dispatch(arg.__class__)(arg, *args, **kwds)
+
+
+@overload
+def just_dispatch(function: Callable[..., R], /) -> JustDispatch[R]: ...
+@overload
+def just_dispatch(*, upper_bound: type[Any] = object) -> Deferred: ...
+def just_dispatch(
+    function: Callable[..., R] | None = None, /, *, upper_bound: type[Any] = object
+) -> JustDispatch[R] | Deferred:
+    """Transform a function into a single-dispatch generic function.
+
+    An alternative take on [`@functools.singledispatch`]:
+    - without [MRO] fallback
+    - allows [*just*] the types registered and optionally an `upper_bound`
+
+    Arguments:
+        function: Function to decorate, where the body serves as the default implementation.
+        upper_bound: When there is no registered implementation for a specific type, it must
+            be a subclass of `upper_bound` to use the default implementation.
+
+    Tip:
+        `@just_dispatch` should only be used to decorate **internal functions** as we lose the docstring.
+
+    [`@functools.singledispatch`]: https://docs.python.org/3/library/functools.html#functools.singledispatch
+    [MRO]: https://docs.python.org/3/howto/mro.html#python-2-3-mro
+    [*just*]: https://github.com/jorenham/optype/blob/e7221ed1d3d02989d5d01873323bac9f88459f26/README.md#just
+    """
+    if function is not None:
+        return JustDispatch(function, upper_bound)
+    return partial(JustDispatch[Any], upper_bound=upper_bound)
diff --git a/narwhals/dtypes/_supertyping.py b/narwhals/dtypes/_supertyping.py
index df0df15835..d534f2bf93 100644
--- a/narwhals/dtypes/_supertyping.py
+++ b/narwhals/dtypes/_supertyping.py
@@ -13,9 +13,10 @@
 from collections import deque
 from itertools import chain, product
 from operator import attrgetter
-from typing import TYPE_CHECKING, Any, Final, Generic, cast
+from typing import TYPE_CHECKING, Any
 
 from narwhals._constants import MS_PER_SECOND, NS_PER_SECOND, US_PER_SECOND
+from narwhals._dispatch import just_dispatch
 from narwhals._typing_compat import TypeVar
 from narwhals.dtypes._classes import (
     Array,
@@ -56,7 +57,6 @@
 
     from typing_extensions import TypeAlias, TypeIs
 
-    from narwhals.dtypes import IntegerType
     from narwhals.dtypes._classes import _Bits
     from narwhals.typing import TimeUnit
 
@@ -72,33 +72,11 @@ def lru_cache(*, maxsize: int) -> Callable[[_Fn], _Fn]:  # noqa: ARG001
 else:
     from functools import cache, lru_cache
 
-Incomplete: TypeAlias = Any
 FrozenDTypes: TypeAlias = frozenset[type[DType]]
 DTypeGroup: TypeAlias = frozenset[type[DType]]
-Nested: TypeAlias = "Array | List | Struct"
-Parametric: TypeAlias = (
-    "Datetime | DatetimeV1 | Decimal |Duration | DurationV1 | Enum | Nested"
-)
 SameTemporalT = TypeVar("SameTemporalT", Datetime, DatetimeV1, Duration, DurationV1)
 """Temporal data types, with a `time_unit` attribute."""
-
 SameDatetimeT = TypeVar("SameDatetimeT", Datetime, DatetimeV1)
-SameT = TypeVar(
-    "SameT",
-    Array,
-    List,
-    Struct,
-    Datetime,
-    DatetimeV1,
-    Decimal,
-    Duration,
-    DurationV1,
-    Enum,
-)
-DTypeT1 = TypeVar("DTypeT1", bound=DType)
-DTypeT2 = TypeVar("DTypeT2", bound=DType, default=DTypeT1)
-DTypeT1_co = TypeVar("DTypeT1_co", bound=DType, covariant=True)
-DTypeT2_co = TypeVar("DTypeT2_co", bound=DType, covariant=True, default=DTypeT1_co)
 
 
 def frozen_dtypes(*dtypes: type[DType]) -> FrozenDTypes:
@@ -145,14 +123,6 @@ def _key_fn_time_unit(obj: Datetime | Duration, /) -> int:
     return _TIME_UNIT_PER_SECOND[obj.time_unit]
 
 
-@lru_cache(maxsize=_CACHE_SIZE * 2)
-def downcast_time_unit(
-    left: SameTemporalT, right: SameTemporalT, /
-) -> SameTemporalT | None:
-    """Return the operand with the lowest precision time unit."""
-    return min(left, right, key=_key_fn_time_unit)
-
-
 @lru_cache(maxsize=_CACHE_SIZE // 2)
 def dtype_eq(left: DType, right: DType, /) -> bool:
     return left == right
@@ -216,6 +186,18 @@ def has_inner(dtype: Any) -> TypeIs[Array | List]:
     return isinstance(dtype, (Array, List))
 
 
+@just_dispatch(upper_bound=DType)
+def same_supertype(left: DType, right: DType, /) -> DType | None:
+    return left if dtype_eq(left, right) else None
+
+
+@same_supertype.register(Duration, DurationV1)
+@lru_cache(maxsize=_CACHE_SIZE * 2)
+def downcast_time_unit(left: SameTemporalT, right: SameTemporalT, /) -> SameTemporalT:
+    """Return the operand with the lowest precision time unit."""
+    return min(left, right, key=_key_fn_time_unit)
+
+
 def _struct_fields_union(
     left: Collection[Field], right: Collection[Field], /
 ) -> Struct | None:
@@ -233,7 +215,8 @@ def _struct_fields_union(
     return Struct(longest_map)
 
 
-def _struct_supertype(left: Struct, right: Struct, /) -> Struct | None:
+@same_supertype.register(Struct)
+def struct_supertype(left: Struct, right: Struct, /) -> Struct | None:
     """Get the supertype of two struct data types.
 
     Adapted from [`super_type_structs`](https://github.com/pola-rs/polars/blob/c2412600210a21143835c9dfcb0a9182f462b619/crates/polars-core/src/utils/supertype.rs#L588-L603)
@@ -252,7 +235,8 @@ def _struct_supertype(left: Struct, right: Struct, /) -> Struct | None:
     return Struct(new_fields)
 
 
-def _array_supertype(left: Array, right: Array, /) -> Array | None:
+@same_supertype.register(Array)
+def array_supertype(left: Array, right: Array, /) -> Array | None:
     if (left.shape == right.shape) and (
         inner := get_supertype(left.inner(), right.inner())
     ):
@@ -260,13 +244,15 @@ def _array_supertype(left: Array, right: Array, /) -> Array | None:
     return None
 
 
-def _list_supertype(left: List, right: List, /) -> List | None:
+@same_supertype.register(List)
+def list_supertype(left: List, right: List, /) -> List | None:
     if inner := get_supertype(left.inner(), right.inner()):
         return List(inner)
     return None
 
 
-def _datetime_supertype(
+@same_supertype.register(Datetime, DatetimeV1)
+def datetime_supertype(
     left: SameDatetimeT, right: SameDatetimeT, /
 ) -> SameDatetimeT | None:
     if left.time_zone != right.time_zone:
@@ -274,62 +260,23 @@ def _datetime_supertype(
     return downcast_time_unit(left, right)
 
 
-def _enum_supertype(left: Enum, right: Enum, /) -> Enum | None:
+@same_supertype.register(Enum)
+def enum_supertype(left: Enum, right: Enum, /) -> Enum | None:
     return left if left.categories == right.categories else None
 
 
-def _decimal_supertype(left: Decimal, right: Decimal, /) -> Decimal:
+@same_supertype.register(Decimal)
+def decimal_supertype(left: Decimal, right: Decimal, /) -> Decimal:
     # https://github.com/pola-rs/polars/blob/529f7ec642912a2f15656897d06f1532c2f5d4c4/crates/polars-core/src/utils/supertype.rs#L508-L511
     precision = max(left.precision, right.precision)
     scale = max(left.scale, right.scale)
     return Decimal(precision=precision, scale=scale)
 
 
-_SAME_DISPATCH: Final[Mapping[type[Parametric], Callable[..., Incomplete | None]]] = {
-    Array: _array_supertype,
-    List: _list_supertype,
-    Struct: _struct_supertype,
-    Datetime: _datetime_supertype,
-    DatetimeV1: _datetime_supertype,
-    Duration: downcast_time_unit,
-    DurationV1: downcast_time_unit,
-    Enum: _enum_supertype,
-    Decimal: _decimal_supertype,
-}
-"""Specialized supertyping rules for `(T, T)`.
-
-*When operands share the same class*, all other data types can use `DType.__eq__` (see [#3393]).
-
-[#3393]: https://github.com/narwhals-dev/narwhals/pull/3393
-"""
-
-
-def is_single_base_type(
-    st: _SupertypeCase[DTypeT1, DType],
-) -> TypeIs[_SupertypeCase[DTypeT1]]:
-    return len(st.base_types) == 1
-
-
-def is_parametric_case(
-    st: _SupertypeCase[SameT | DType],
-) -> TypeIs[_SupertypeCase[SameT]]:
-    return st.base_left in _SAME_DISPATCH
-
-
-def _get_same_supertype_fn(base: type[SameT]) -> Callable[[SameT, SameT], SameT | None]:
-    return cast("Callable[[SameT, SameT], SameT | None]", _SAME_DISPATCH[base])
-
-
-def _same_supertype(st: _SupertypeCase[SameT | DType]) -> SameT | DType | None:
-    if is_parametric_case(st):
-        return _get_same_supertype_fn(st.base_left)(st.left, st.right)
-    return st.left if dtype_eq(st.left, st.right) else None
-
-
 DEC128_MAX_PREC = 38
 # Precomputing powers of 10 up to 10^38
 POW10_LIST = tuple(10**i for i in range(DEC128_MAX_PREC + 1))
-INT_MAX_MAP: Mapping[IntegerType, int] = {
+INT_MAX_MAP: Mapping[Int, int] = {
     UInt8(): (2**8) - 1,
     UInt16(): (2**16) - 1,
     UInt32(): (2**32) - 1,
@@ -349,7 +296,7 @@ def _integer_fits_in_decimal(value: int, precision: int, scale: int) -> bool:
     )
 
 
-def _decimal_integer_supertyping(decimal: Decimal, integer: IntegerType) -> DType | None:
+def _decimal_integer_supertyping(decimal: Decimal, integer: Int) -> DType | None:
     precision, scale = decimal.precision, decimal.scale
 
     if integer in {UInt128(), Int128()}:
@@ -364,15 +311,15 @@ def _decimal_integer_supertyping(decimal: Decimal, integer: IntegerType) -> DTyp
     return Decimal(precision, scale)
 
 
-@lru_cache(maxsize=_CACHE_SIZE)
-def _numeric_supertype(st: _SupertypeCase[DType]) -> DType | None:
+def _numeric_supertype(
+    left: DType, right: DType, base_types: FrozenDTypes
+) -> DType | None:
     """Get the supertype of two numeric data types that do not share the same class.
 
     `_{primitive_numeric,integer}_supertyping` define most valid numeric supertypes.
 
     We generate these on first use, with all subsequent calls returning the same mapping.
     """
-    base_types = st.base_types
     if NUMERIC.issuperset(base_types):
         if INTEGER.issuperset(base_types):
             return _integer_supertyping()[base_types]()
@@ -382,9 +329,7 @@ def _numeric_supertype(st: _SupertypeCase[DType]) -> DType | None:
             # Logic adapted from rust implementation
             # https://github.com/pola-rs/polars/blob/529f7ec642912a2f15656897d06f1532c2f5d4c4/crates/polars-core/src/utils/supertype.rs#L517-L530
             decimal, integer = (
-                (st.left, st.right)
-                if isinstance(st.left, Decimal)
-                else (st.right, st.left)
+                (left, right) if isinstance(left, Decimal) else (right, left)
             )
             return _decimal_integer_supertyping(decimal=decimal, integer=integer)  # type: ignore[arg-type]
 
@@ -404,47 +349,24 @@ def _mixed_nested_supertype(left: DType, right: DType, /) -> DType | None:
     return None
 
 
-def _mixed_supertype(st: _SupertypeCase[DType, DType]) -> DType | None:
+def _mixed_supertype(
+    left: DType, right: DType, base_types: FrozenDTypes, /
+) -> DType | None:
     """Get the supertype of two data types that do not share the same class."""
-    base_types = st.base_types
-    left, right = st.left, st.right
     if Date in base_types and _has_intersection(base_types, DATETIME):
         return left if isinstance(left, Datetime) else right
     if String in base_types:
         return (Binary if Binary in base_types else String)()
     if has_nested(base_types):
         return _mixed_nested_supertype(left, right)
-    return _numeric_supertype(st) if _has_intersection(NUMERIC, base_types) else None
-
-
-class _SupertypeCase(Generic[DTypeT1_co, DTypeT2_co]):
-    """WIP."""
-
-    __slots__ = ("base_types", "left", "right")
-
-    left: DTypeT1_co
-    right: DTypeT2_co
-    base_types: frozenset[type[DTypeT1_co | DTypeT2_co]]
-
-    def __init__(self, left: DTypeT1_co, right: DTypeT2_co) -> None:
-        self.left = left
-        self.right = right
-        self.base_types = frozenset((self.base_left, self.base_right))
-
-    @property
-    def base_left(self) -> type[DTypeT1_co]:
-        return self.left.base_type()
-
-    @property
-    def base_right(self) -> type[DTypeT2_co]:
-        return self.right.base_type()
+    return (
+        _numeric_supertype(left, right, base_types)
+        if _has_intersection(NUMERIC, base_types)
+        else None
+    )
 
 
-# NOTE @dangotbanned: Tried **many** variants of this typing
-# (to self) DO NOT TOUCH IT AGAIN
-def get_supertype(
-    left: DTypeT1, right: DTypeT2 | DType
-) -> DTypeT1 | DTypeT2 | DType | None:
+def get_supertype(left: DType, right: DType) -> DType | None:
     """Given two data types, determine the data type that both types can reasonably safely be cast to.
 
     Arguments:
@@ -454,9 +376,9 @@ def get_supertype(
     Returns:
         The common supertype that both types can be safely cast to, or None if no such type exists.
     """
-    st_case = _SupertypeCase(left, right)
-    if Unknown in st_case.base_types:
+    base_types = frozen_dtypes(left.base_type(), right.base_type())
+    if Unknown in base_types:
         return Unknown()
-    if is_single_base_type(st_case):
-        return _same_supertype(st_case)
-    return _mixed_supertype(st_case)
+    if len(base_types) == 1:
+        return same_supertype(left, right)
+    return _mixed_supertype(left, right, base_types)
diff --git a/tests/dispatch_test.py b/tests/dispatch_test.py
new file mode 100644
index 0000000000..2745ba6bf4
--- /dev/null
+++ b/tests/dispatch_test.py
@@ -0,0 +1,106 @@
+from __future__ import annotations
+
+import decimal
+import string
+
+import pytest
+
+import narwhals as nw
+import narwhals.stable.v1 as nw_v1
+from narwhals._dispatch import JustDispatch, just_dispatch
+from narwhals.dtypes import DType, SignedIntegerType
+
+
+def type_name(obj: object) -> str:
+    return type(obj).__name__
+
+
+@pytest.fixture
+def dispatch_no_bound() -> JustDispatch[str]:
+    @just_dispatch
+    def dtype_repr_code(dtype: DType) -> str:
+        return type_name(dtype).lower()
+
+    return dtype_repr_code
+
+
+@pytest.fixture
+def dispatch_upper_bound() -> JustDispatch[str]:
+    @just_dispatch(upper_bound=DType)
+    def dtype_repr_code(dtype: DType) -> str:
+        return type_name(dtype).lower()
+
+    return dtype_repr_code
+
+
+@pytest.fixture
+def stdlib_decimal() -> decimal.Decimal:
+    return decimal.Decimal("1.0")
+
+
+def test_just_dispatch(
+    dispatch_no_bound: JustDispatch[str], stdlib_decimal: decimal.Decimal
+) -> None:
+    i64 = nw.Int64()
+    assert dispatch_no_bound(i64) == "int64"
+
+    @dispatch_no_bound.register(*SignedIntegerType.__subclasses__())
+    def repr_int(dtype: SignedIntegerType) -> str:
+        return f"i{type_name(dtype).strip(string.ascii_letters)}"
+
+    assert dispatch_no_bound(i64) == "i64"
+    assert repr_int(i64) == "i64"
+    assert dispatch_no_bound(nw.UInt8()) == "uint8"
+    assert dispatch_no_bound(stdlib_decimal) == "decimal"
+
+
+def test_just_dispatch_upper_bound(
+    dispatch_upper_bound: JustDispatch[str], stdlib_decimal: decimal.Decimal
+) -> None:
+    i64 = nw.Int64()
+    assert dispatch_upper_bound(i64) == "int64"
+
+    @dispatch_upper_bound.register(*SignedIntegerType.__subclasses__())
+    def repr_int(dtype: SignedIntegerType) -> str:
+        return f"i{type_name(dtype).strip(string.ascii_letters)}"
+
+    assert dispatch_upper_bound(i64) == "i64"
+    assert repr_int(i64) == "i64"
+    assert dispatch_upper_bound(nw.UInt8()) == "uint8"
+    assert dispatch_upper_bound(nw.Decimal()) == "decimal"
+
+    with pytest.raises(TypeError, match=r"'dtype_repr_code' does not support 'Decimal'"):
+        dispatch_upper_bound(stdlib_decimal)
+
+    dispatch_upper_bound.register(type(stdlib_decimal))(lambda _: "need to be explicit")
+    assert dispatch_upper_bound(stdlib_decimal) == "need to be explicit"
+
+
+def test_just_dispatch_no_auto_subclass(dispatch_no_bound: JustDispatch[str]) -> None:
+    NOT_REGISTERED = "datetime"  # noqa: N806
+    TZ = "Africa/Accra"  # noqa: N806
+
+    assert dispatch_no_bound(nw.Datetime("ms")) == NOT_REGISTERED
+    assert dispatch_no_bound(nw_v1.Datetime("us")) == NOT_REGISTERED
+
+    @dispatch_no_bound.register(nw.Datetime)
+    def repr_datetime(dtype: nw.Datetime) -> str:
+        if dtype.time_zone is None:
+            args: str = dtype.time_unit
+        else:
+            args = f"{dtype.time_unit}, {dtype.time_zone}"
+        return f"datetime[{args}]"
+
+    assert dispatch_no_bound(nw.Datetime()) == "datetime[us]"
+    assert dispatch_no_bound(nw.Datetime("s")) == "datetime[s]"
+    assert dispatch_no_bound(nw.Datetime(time_zone=TZ)) == f"datetime[us, {TZ}]"
+
+    assert dispatch_no_bound(nw_v1.Datetime()) == NOT_REGISTERED
+    assert dispatch_no_bound(nw_v1.Datetime("s")) == NOT_REGISTERED
+    assert dispatch_no_bound(nw_v1.Datetime(time_zone=TZ)) == NOT_REGISTERED
+
+    dispatch_no_bound.register(nw_v1.Datetime)(repr_datetime)
+
+    assert dispatch_no_bound(nw_v1.Datetime()) == "datetime[us]"
+    assert dispatch_no_bound(nw_v1.Datetime("s")) == "datetime[s]"
+    assert dispatch_no_bound(nw_v1.Datetime(time_zone=TZ)) == f"datetime[us, {TZ}]"