diff --git a/playground/TestPlatform.Playground/TestPlatform.Playground.csproj b/playground/TestPlatform.Playground/TestPlatform.Playground.csproj
index da802a6e46..d73746f16e 100644
--- a/playground/TestPlatform.Playground/TestPlatform.Playground.csproj
+++ b/playground/TestPlatform.Playground/TestPlatform.Playground.csproj
@@ -2,6 +2,9 @@
   <PropertyGroup>
     <TestPlatformRoot Condition="$(TestPlatformRoot) == ''">..\..\</TestPlatformRoot>
     <TargetLatestRuntimePatch>true</TargetLatestRuntimePatch>
+    <!-- MSB3270 Suppress warnings about testhost being x64 (AMD64)/x86 when imported into AnyCPU (MSIL) projects. -->
+    <!-- MSB3276 Suppress warnings about conflicts between different versions of the same dependent assembly -->
+    <MSBuildWarningsAsMessages>$(MSBuildWarningsAsMessages);MSB3270;MSB3276</MSBuildWarningsAsMessages>
   </PropertyGroup>
 
   <Import Project="$(TestPlatformRoot)scripts/build/TestPlatform.Settings.targets" />
diff --git a/scripts/build/TestPlatform.Settings.targets b/scripts/build/TestPlatform.Settings.targets
index b032060b56..2539dc660b 100644
--- a/scripts/build/TestPlatform.Settings.targets
+++ b/scripts/build/TestPlatform.Settings.targets
@@ -68,6 +68,8 @@
     <When Condition="$(TestProject) == 'true'">
       <PropertyGroup>
         <GenerateDocumentationFile>false</GenerateDocumentationFile>
+        <!-- Suppress warnings about testhost being x64 (AMD64)/x86 when imported into AnyCPU (MSIL) test projects. -->
+        <NoWarn>$(NoWarn);MSB3270</NoWarn>
       </PropertyGroup>
 
       <!-- Test projects are not discovered in test window without test container capability -->
diff --git a/src/Microsoft.TestPlatform.Extensions.BlameDataCollector/Microsoft.TestPlatform.Extensions.BlameDataCollector.csproj b/src/Microsoft.TestPlatform.Extensions.BlameDataCollector/Microsoft.TestPlatform.Extensions.BlameDataCollector.csproj
index 31dcf3aa46..e5e98be5ad 100644
--- a/src/Microsoft.TestPlatform.Extensions.BlameDataCollector/Microsoft.TestPlatform.Extensions.BlameDataCollector.csproj
+++ b/src/Microsoft.TestPlatform.Extensions.BlameDataCollector/Microsoft.TestPlatform.Extensions.BlameDataCollector.csproj
@@ -1,6 +1,15 @@
 <?xml version="1.0" encoding="utf-8"?>
 <Project Sdk="Microsoft.NET.Sdk">
   <PropertyGroup>
+    <!-- NU1702 suppresses warning about DumpMinitool being .NET Framework reference imported to a .NET project.
+    Unfortunately this can't be suppressed at single ProjectReference. Neither completely suppressed by using NoWarn.
+    Workaround is documented here: https://github.com/NuGet/Home/issues/8093, but this syntax and placement would be preferred:
+    https://github.com/dotnet/core/issues/869
+    -->
+    <MSBuildWarningsAsMessages>$(MSBuildWarningsAsMessages);NU1702</MSBuildWarningsAsMessages>
+    <!-- MSB3270 Suppress warnings about testhost being x64 (AMD64)/x86 when imported into AnyCPU (MSIL) projects. -->
+    <!-- MSB3276 Suppress warnings about conflicts between different versions of the same dependent assembly -->
+    <MSBuildWarningsAsMessages>$(MSBuildWarningsAsMessages);MSB3270;MSB3276</MSBuildWarningsAsMessages>
     <TestPlatformRoot Condition="$(TestPlatformRoot) == ''">..\..\</TestPlatformRoot>
   </PropertyGroup>
   <Import Project="$(TestPlatformRoot)scripts/build/TestPlatform.Settings.targets" />
diff --git a/src/Microsoft.TestPlatform.PlatformAbstractions/Microsoft.TestPlatform.PlatformAbstractions.csproj b/src/Microsoft.TestPlatform.PlatformAbstractions/Microsoft.TestPlatform.PlatformAbstractions.csproj
index c4216da53e..e927847a2a 100644
--- a/src/Microsoft.TestPlatform.PlatformAbstractions/Microsoft.TestPlatform.PlatformAbstractions.csproj
+++ b/src/Microsoft.TestPlatform.PlatformAbstractions/Microsoft.TestPlatform.PlatformAbstractions.csproj
@@ -12,7 +12,7 @@
     <TargetFrameworks Condition=" '$(DotNetBuildFromSource)' == 'true' ">net6.0</TargetFrameworks>
     <IsTestProject>false</IsTestProject>
     <!-- This causes a build error on netcoreapp1.0 -->
-    <NoWarn Condition="'$(TargetFramework)' != 'netcoreapp1.0'">NU1605</NoWarn>
+    <NoWarn Condition="'$(TargetFramework)' != 'netcoreapp1.0'">$(NoWarn);NU1605</NoWarn>
   </PropertyGroup>
 
   <PropertyGroup Condition="'$(TargetFramework)' == 'uap10.0'">
diff --git a/src/testhost.x86/testhost.x86.csproj b/src/testhost.x86/testhost.x86.csproj
index b17fe654e2..064b619c64 100644
--- a/src/testhost.x86/testhost.x86.csproj
+++ b/src/testhost.x86/testhost.x86.csproj
@@ -3,6 +3,9 @@
   <PropertyGroup>
     <TestPlatformRoot Condition="$(TestPlatformRoot) == ''">..\..\</TestPlatformRoot>
     <TargetLatestRuntimePatch>true</TargetLatestRuntimePatch>
+    <!-- MSB3270 Suppress warnings about testhost being x64 (AMD64)/x86 when imported into AnyCPU (MSIL) projects. -->
+    <!-- MSB3276 Suppress warnings about conflicts between different versions of the same dependent assembly -->
+    <MSBuildWarningsAsMessages>$(MSBuildWarningsAsMessages);MSB3270;MSB3276</MSBuildWarningsAsMessages>
   </PropertyGroup>
   <Import Project="$(TestPlatformRoot)src\Microsoft.TestPlatform.Execution.Shared\Microsoft.TestPlatform.Execution.Shared.projitems" Label="Shared" />
   <Import Project="$(TestPlatformRoot)scripts/build/TestPlatform.Settings.targets" />
diff --git a/src/testhost/testhost.csproj b/src/testhost/testhost.csproj
index fabffdd89a..128ebcf677 100644
--- a/src/testhost/testhost.csproj
+++ b/src/testhost/testhost.csproj
@@ -3,6 +3,9 @@
   <PropertyGroup>
     <TestPlatformRoot Condition="$(TestPlatformRoot) == ''">..\..\</TestPlatformRoot>
     <TargetLatestRuntimePatch>true</TargetLatestRuntimePatch>
+    <!-- MSB3270 Suppress warnings about testhost being x64 (AMD64)/x86 when imported into AnyCPU (MSIL) projects. -->
+    <!-- MSB3276 Suppress warnings about conflicts between different versions of the same dependent assembly -->
+    <MSBuildWarningsAsMessages>$(MSBuildWarningsAsMessages);MSB3270;MSB3276</MSBuildWarningsAsMessages>
   </PropertyGroup>
   <Import Project="$(TestPlatformRoot)src\Microsoft.TestPlatform.Execution.Shared\Microsoft.TestPlatform.Execution.Shared.projitems" Label="Shared" />
   <Import Project="$(TestPlatformRoot)scripts/build/TestPlatform.Settings.targets" />
diff --git a/test/Microsoft.TestPlatform.Extensions.BlameDataCollector.UnitTests/Microsoft.TestPlatform.Extensions.BlameDataCollector.UnitTests.csproj b/test/Microsoft.TestPlatform.Extensions.BlameDataCollector.UnitTests/Microsoft.TestPlatform.Extensions.BlameDataCollector.UnitTests.csproj
index e447138d78..0024aa19b4 100644
--- a/test/Microsoft.TestPlatform.Extensions.BlameDataCollector.UnitTests/Microsoft.TestPlatform.Extensions.BlameDataCollector.UnitTests.csproj
+++ b/test/Microsoft.TestPlatform.Extensions.BlameDataCollector.UnitTests/Microsoft.TestPlatform.Extensions.BlameDataCollector.UnitTests.csproj
@@ -4,6 +4,15 @@
     <TestPlatformRoot Condition="$(TestPlatformRoot) == ''">..\..\</TestPlatformRoot>
     <TestProject>true</TestProject>
     <IsTestProject>true</IsTestProject>
+    <!-- NU1702 suppresses warning about testhost being .NET Framework reference imported to a .NET project.
+    Unfortunately this can't be suppressed at single ProjectReference. Neither completely suppressed by using NoWarn.
+    Workaround is documented here: https://github.com/NuGet/Home/issues/8093, but this syntax and placement would be preferred:
+    https://github.com/dotnet/core/issues/869
+    -->
+    <MSBuildWarningsAsMessages>$(MSBuildWarningsAsMessages);NU1702</MSBuildWarningsAsMessages>
+    <!-- MSB3270 Suppress warnings about testhost being x64 (AMD64)/x86 when imported into AnyCPU (MSIL) projects. -->
+    <!-- MSB3276 Suppress warnings about conflicts between different versions of the same dependent assembly -->
+    <MSBuildWarningsAsMessages>$(MSBuildWarningsAsMessages);MSB3270;MSB3276</MSBuildWarningsAsMessages>
   </PropertyGroup>
   <Import Project="$(TestPlatformRoot)scripts/build/TestPlatform.Settings.targets" />
   <PropertyGroup Label="Configuration">