diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 6bf56c4e30..bc31281db5 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -712,7 +712,7 @@ jobs:
 
         include:
           - python: 3.9
-            args: -DCMAKE_CXX_STANDARD=20 -DDOWNLOAD_EIGEN=OFF
+            args: -DCMAKE_CXX_STANDARD=20
           - python: 3.8
             args: -DCMAKE_CXX_STANDARD=17
 
@@ -835,7 +835,7 @@ jobs:
         cmake -S . -B build
         -DPYBIND11_WERROR=ON
         -DDOWNLOAD_CATCH=ON
-        -DDOWNLOAD_EIGEN=OFF
+        -DDOWNLOAD_EIGEN=ON
         -DCMAKE_CXX_STANDARD=20
 
     - name: Build C++20
diff --git a/include/pybind11/detail/common.h b/include/pybind11/detail/common.h
index 1070d686ec..1d4939bed7 100644
--- a/include/pybind11/detail/common.h
+++ b/include/pybind11/detail/common.h
@@ -822,7 +822,9 @@ struct is_template_base_of_impl {
 /// Check if a template is the base of a type. For example:
 /// `is_template_base_of<Base, T>` is true if `struct T : Base<U> {}` where U can be anything
 template <template <typename...> class Base, typename T>
-#if defined(PYBIND11_CPP20) || !defined(_MSC_VER) // Sadly, all MSVC versions incl. 2022 need this.
+// Sadly, all MSVC versions incl. 2022 need the workaround, even in C++20 mode.
+// See also: https://github.com/pybind/pybind11/pull/3741
+#if !defined(_MSC_VER)
 using is_template_base_of
     = decltype(is_template_base_of_impl<Base>::check((intrinsic_t<T> *) nullptr));
 #else
diff --git a/include/pybind11/eigen.h b/include/pybind11/eigen.h
index 47820ce895..930c4f7fa8 100644
--- a/include/pybind11/eigen.h
+++ b/include/pybind11/eigen.h
@@ -21,10 +21,12 @@
 // make it version specific, or even remove it later, but considering that
 // 1. C4127 is generally far more distracting than useful for modern template code, and
 // 2. we definitely want to ignore any MSVC warnings originating from Eigen code,
-// it is probably best to keep this around indefinitely.
+//    it is probably best to keep this around indefinitely.
 #if defined(_MSC_VER)
 #    pragma warning(push)
 #    pragma warning(disable : 4127) // C4127: conditional expression is constant
+#    pragma warning(disable : 5054) // https://github.com/pybind/pybind11/pull/3741
+//       C5054: operator '&': deprecated between enumerations of different types
 #endif
 
 #include <Eigen/Core>