diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 6e0ffa63a..38b85aeef 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -904,8 +904,7 @@ jobs:
           - { sys: mingw64, env: x86_64 }
           - { sys: mingw32, env: i686 }
     steps:
-    # Force version because of https://github.com/msys2/setup-msys2/issues/167
-    - uses: msys2/setup-msys2@v2.4.2
+    - uses: msys2/setup-msys2@v2
       with:
         msystem: ${{matrix.sys}}
         install: >-
@@ -935,10 +934,10 @@ jobs:
       run: cmake --build build --target pytest -j 2
 
     - name: C++11 tests
-      run: cmake --build build --target cpptest -j 2
+      run: PYTHONHOME=/${{matrix.sys}} PYTHONPATH=/${{matrix.sys}} cmake --build build --target cpptest -j 2
 
     - name: Interface test C++11
-      run: cmake --build build --target test_cmake_build
+      run: PYTHONHOME=/${{matrix.sys}} PYTHONPATH=/${{matrix.sys}} cmake --build build --target test_cmake_build
 
     - name: Clean directory
       run: git clean -fdx
@@ -953,10 +952,10 @@ jobs:
       run: cmake --build build2 --target pytest -j 2
 
     - name: C++14 tests
-      run: cmake --build build2 --target cpptest -j 2
+      run: PYTHONHOME=/${{matrix.sys}} PYTHONPATH=/${{matrix.sys}} cmake --build build2 --target cpptest -j 2
 
     - name: Interface test C++14
-      run: cmake --build build2 --target test_cmake_build
+      run: PYTHONHOME=/${{matrix.sys}} PYTHONPATH=/${{matrix.sys}} cmake --build build2 --target test_cmake_build
 
     - name: Clean directory
       run: git clean -fdx
@@ -971,7 +970,7 @@ jobs:
       run: cmake --build build3 --target pytest -j 2
 
     - name: C++17 tests
-      run: cmake --build build3 --target cpptest -j 2
+      run: PYTHONHOME=/${{matrix.sys}} PYTHONPATH=/${{matrix.sys}} cmake --build build3 --target cpptest -j 2
 
     - name: Interface test C++17
-      run: cmake --build build3 --target test_cmake_build
+      run: PYTHONHOME=/${{matrix.sys}} PYTHONPATH=/${{matrix.sys}} cmake --build build3 --target test_cmake_build
diff --git a/docs/advanced/classes.rst b/docs/advanced/classes.rst
index 6330af5eb..ba006252a 100644
--- a/docs/advanced/classes.rst
+++ b/docs/advanced/classes.rst
@@ -9,7 +9,7 @@ that you are already familiar with the basics from :doc:`/classes`.
 Overriding virtual functions in Python
 ======================================
 
-Suppose that a C++ class or interface has a virtual function that we'd like to
+Suppose that a C++ class or interface has a virtual function that we'd like
 to override from within Python (we'll focus on the class ``Animal``; ``Dog`` is
 given as a specific example of how one would do this with traditional C++
 code).
diff --git a/include/pybind11/pybind11.h b/include/pybind11/pybind11.h
index 344a18c56..df33d5182 100644
--- a/include/pybind11/pybind11.h
+++ b/include/pybind11/pybind11.h
@@ -1206,10 +1206,13 @@ protected:
         if (rec.bases.size() > 1 || rec.multiple_inheritance) {
             mark_parents_nonsimple(tinfo->type);
             tinfo->simple_ancestors = false;
+            tinfo->simple_type = false;
         }
         else if (rec.bases.size() == 1) {
             auto parent_tinfo = get_type_info((PyTypeObject *) rec.bases[0].ptr());
             tinfo->simple_ancestors = parent_tinfo->simple_ancestors;
+            // a child of a non-simple type can never be a simple type
+            tinfo->simple_type = parent_tinfo->simple_type;
         }
 
         if (rec.module_local) {
diff --git a/tests/test_multiple_inheritance.cpp b/tests/test_multiple_inheritance.cpp
index 6963197a5..44b9876eb 100644
--- a/tests/test_multiple_inheritance.cpp
+++ b/tests/test_multiple_inheritance.cpp
@@ -230,4 +230,87 @@ TEST_SUBMODULE(multiple_inheritance, m) {
         .def("c1", [](C1 *self) { return self; });
     py::class_<D, C0, C1>(m, "D")
         .def(py::init<>());
+
+    // test_pr3635_diamond_*
+    // - functions are get_{base}_{var}, return {var}
+    struct MVB {
+        MVB() = default;
+        MVB(const MVB&) = default;
+        virtual ~MVB() = default;
+
+        int b = 1;
+        int get_b_b() const { return b; }
+    };
+    struct MVC : virtual MVB {
+        int c = 2;
+        int get_c_b() const { return b; }
+        int get_c_c() const { return c; }
+    };
+    struct MVD0 : virtual MVC {
+        int d0 = 3;
+        int get_d0_b() const { return b; }
+        int get_d0_c() const { return c; }
+        int get_d0_d0() const { return d0; }
+    };
+    struct MVD1 : virtual MVC {
+        int d1 = 4;
+        int get_d1_b() const { return b; }
+        int get_d1_c() const { return c; }
+        int get_d1_d1() const { return d1; }
+    };
+    struct MVE : virtual MVD0, virtual MVD1 {
+        int e = 5;
+        int get_e_b() const { return b; }
+        int get_e_c() const { return c; }
+        int get_e_d0() const { return d0; }
+        int get_e_d1() const { return d1; }
+        int get_e_e() const { return e; }
+    };
+    struct MVF : virtual MVE {
+        int f = 6;
+        int get_f_b() const { return b; }
+        int get_f_c() const { return c; }
+        int get_f_d0() const { return d0; }
+        int get_f_d1() const { return d1; }
+        int get_f_e() const { return e; }
+        int get_f_f() const { return f; }
+    };
+    py::class_<MVB>(m, "MVB")
+        .def(py::init<>())
+        .def("get_b_b", &MVB::get_b_b)
+        .def_readwrite("b", &MVB::b);
+    py::class_<MVC, MVB>(m, "MVC")
+        .def(py::init<>())
+        .def("get_c_b", &MVC::get_c_b)
+        .def("get_c_c", &MVC::get_c_c)
+        .def_readwrite("c", &MVC::c);
+    py::class_<MVD0, MVC>(m, "MVD0")
+        .def(py::init<>())
+        .def("get_d0_b", &MVD0::get_d0_b)
+        .def("get_d0_c", &MVD0::get_d0_c)
+        .def("get_d0_d0", &MVD0::get_d0_d0)
+        .def_readwrite("d0", &MVD0::d0);
+    py::class_<MVD1, MVC>(m, "MVD1")
+        .def(py::init<>())
+        .def("get_d1_b", &MVD1::get_d1_b)
+        .def("get_d1_c", &MVD1::get_d1_c)
+        .def("get_d1_d1", &MVD1::get_d1_d1)
+        .def_readwrite("d1", &MVD1::d1);
+    py::class_<MVE, MVD0, MVD1>(m, "MVE")
+        .def(py::init<>())
+        .def("get_e_b", &MVE::get_e_b)
+        .def("get_e_c", &MVE::get_e_c)
+        .def("get_e_d0", &MVE::get_e_d0)
+        .def("get_e_d1", &MVE::get_e_d1)
+        .def("get_e_e", &MVE::get_e_e)
+        .def_readwrite("e", &MVE::e);
+    py::class_<MVF, MVE>(m, "MVF")
+        .def(py::init<>())
+        .def("get_f_b", &MVF::get_f_b)
+        .def("get_f_c", &MVF::get_f_c)
+        .def("get_f_d0", &MVF::get_f_d0)
+        .def("get_f_d1", &MVF::get_f_d1)
+        .def("get_f_e", &MVF::get_f_e)
+        .def("get_f_f", &MVF::get_f_f)
+        .def_readwrite("f", &MVF::f);
 }
diff --git a/tests/test_multiple_inheritance.py b/tests/test_multiple_inheritance.py
index a02c31300..71741b925 100644
--- a/tests/test_multiple_inheritance.py
+++ b/tests/test_multiple_inheritance.py
@@ -358,3 +358,117 @@ def test_diamond_inheritance():
     assert d is d.c0().b()
     assert d is d.c1().b()
     assert d is d.c0().c1().b().c0().b()
+
+
+def test_pr3635_diamond_b():
+    o = m.MVB()
+    assert o.b == 1
+
+    assert o.get_b_b() == 1
+
+
+def test_pr3635_diamond_c():
+    o = m.MVC()
+    assert o.b == 1
+    assert o.c == 2
+
+    assert o.get_b_b() == 1
+    assert o.get_c_b() == 1
+
+    assert o.get_c_c() == 2
+
+
+def test_pr3635_diamond_d0():
+    o = m.MVD0()
+    assert o.b == 1
+    assert o.c == 2
+    assert o.d0 == 3
+
+    assert o.get_b_b() == 1
+    assert o.get_c_b() == 1
+    assert o.get_d0_b() == 1
+
+    assert o.get_c_c() == 2
+    assert o.get_d0_c() == 2
+
+    assert o.get_d0_d0() == 3
+
+
+def test_pr3635_diamond_d1():
+    o = m.MVD1()
+    assert o.b == 1
+    assert o.c == 2
+    assert o.d1 == 4
+
+    assert o.get_b_b() == 1
+    assert o.get_c_b() == 1
+    assert o.get_d1_b() == 1
+
+    assert o.get_c_c() == 2
+    assert o.get_d1_c() == 2
+
+    assert o.get_d1_d1() == 4
+
+
+def test_pr3635_diamond_e():
+    o = m.MVE()
+    assert o.b == 1
+    assert o.c == 2
+    assert o.d0 == 3
+    assert o.d1 == 4
+    assert o.e == 5
+
+    assert o.get_b_b() == 1
+    assert o.get_c_b() == 1
+    assert o.get_d0_b() == 1
+    assert o.get_d1_b() == 1
+    assert o.get_e_b() == 1
+
+    assert o.get_c_c() == 2
+    assert o.get_d0_c() == 2
+    assert o.get_d1_c() == 2
+    assert o.get_e_c() == 2
+
+    assert o.get_d0_d0() == 3
+    assert o.get_e_d0() == 3
+
+    assert o.get_d1_d1() == 4
+    assert o.get_e_d1() == 4
+
+    assert o.get_e_e() == 5
+
+
+def test_pr3635_diamond_f():
+    o = m.MVF()
+    assert o.b == 1
+    assert o.c == 2
+    assert o.d0 == 3
+    assert o.d1 == 4
+    assert o.e == 5
+    assert o.f == 6
+
+    assert o.get_b_b() == 1
+    assert o.get_c_b() == 1
+    assert o.get_d0_b() == 1
+    assert o.get_d1_b() == 1
+    assert o.get_e_b() == 1
+    assert o.get_f_b() == 1
+
+    assert o.get_c_c() == 2
+    assert o.get_d0_c() == 2
+    assert o.get_d1_c() == 2
+    assert o.get_e_c() == 2
+    assert o.get_f_c() == 2
+
+    assert o.get_d0_d0() == 3
+    assert o.get_e_d0() == 3
+    assert o.get_f_d0() == 3
+
+    assert o.get_d1_d1() == 4
+    assert o.get_e_d1() == 4
+    assert o.get_f_d1() == 4
+
+    assert o.get_e_e() == 5
+    assert o.get_f_e() == 5
+
+    assert o.get_f_f() == 6