diff --git a/lib/systems/default.nix b/lib/systems/default.nix
index e02890b1138..4d5f97aeda0 100644
--- a/lib/systems/default.nix
+++ b/lib/systems/default.nix
@@ -34,8 +34,11 @@ rec {
       # Either of these can be losslessly-extracted from `parsed` iff parsing succeeds.
       system = parse.doubleFromSystem final.parsed;
       config = parse.tripleFromSystem final.parsed;
-      # Determine whether we are compatible with the provided CPU
-      isCompatible = platform: parse.isCompatible final.parsed.cpu platform.parsed.cpu;
+      # Determine whether we can execute binaries built for the provided platform.
+      canExecute = platform:
+        parse.isCompatible final.parsed.cpu platform.parsed.cpu
+        && final.parsed.kernel == platform.parsed.kernel;
+      isCompatible = _: throw "2022-05-23: isCompatible has been removed in favor of canExecute, refer to the 22.11 changelog for details";
       # Derived meta-data
       libc =
         /**/ if final.isDarwin              then "libSystem"
diff --git a/lib/systems/parse.nix b/lib/systems/parse.nix
index bf436ec8db5..9d2571c993a 100644
--- a/lib/systems/parse.nix
+++ b/lib/systems/parse.nix
@@ -148,8 +148,10 @@ rec {
   #   Every CPU is compatible with itself.
   # - (transitivity)
   #   If A is compatible with B and B is compatible with C then A is compatible with C.
-  # - (compatible under multiple endianness)
-  #   CPUs with multiple modes of endianness are pairwise compatible.
+  #
+  # Note: Since 22.11 the archs of a mode switching CPU are no longer considered
+  # pairwise compatible. Mode switching implies that binaries built for A
+  # and B respectively can't be executed at the same time.
   isCompatible = a: b: with cpuTypes; lib.any lib.id [
     # x86
     (b == i386 && isCompatible a i486)
@@ -191,22 +193,13 @@ rec {
     (b == aarch64 && a == armv8a)
     (b == armv8a && isCompatible a aarch64)
 
-    (b == aarch64 && a == aarch64_be)
-    (b == aarch64_be && isCompatible a aarch64)
-
     # PowerPC
     (b == powerpc && isCompatible a powerpc64)
-    (b == powerpcle && isCompatible a powerpc)
-    (b == powerpc && a == powerpcle)
-    (b == powerpc64le && isCompatible a powerpc64)
-    (b == powerpc64 && a == powerpc64le)
+    (b == powerpcle && isCompatible a powerpc64le)
 
     # MIPS
     (b == mips && isCompatible a mips64)
-    (b == mips && a == mipsel)
-    (b == mipsel && isCompatible a mips)
-    (b == mips64 && a == mips64el)
-    (b == mips64el && isCompatible a mips64)
+    (b == mipsel && isCompatible a mips64el)
 
     # RISCV
     (b == riscv32 && isCompatible a riscv64)
diff --git a/nixos/doc/manual/from_md/release-notes/rl-2211.section.xml b/nixos/doc/manual/from_md/release-notes/rl-2211.section.xml
index b34d182183c..4abcf0165a4 100644
--- a/nixos/doc/manual/from_md/release-notes/rl-2211.section.xml
+++ b/nixos/doc/manual/from_md/release-notes/rl-2211.section.xml
@@ -13,8 +13,22 @@
     <itemizedlist spacing="compact">
       <listitem>
         <para>
-          Please remove this line when you add the first item since
-          docbook requires the section to be non-empty
+          During cross-compilation, tests are now executed if the test
+          suite can be executed by the build platform. This is the case
+          when doing “native” cross-compilation where the build and host
+          platforms are largely the same, but the nixpkgs’ cross
+          compilation infrastructure is used, e.g.
+          <literal>pkgsStatic</literal> and <literal>pkgsLLVM</literal>.
+          Another possibility is that the build platform is a superset
+          of the host platform, e.g. when cross-compiling from
+          <literal>x86_64-unknown-linux</literal> to
+          <literal>i686-unknown-linux</literal>. The predicate gating
+          test suite execution is the newly added
+          <literal>canExecute</literal> predicate: You can e.g. check if
+          <literal>stdenv.buildPlatform</literal> can execute binaries
+          built for <literal>stdenv.hostPlatform</literal> (i.e.
+          produced by <literal>stdenv.cc</literal>) by evaluating
+          <literal>stdenv.buildPlatform.canExecute stdenv.hostPlatform</literal>.
         </para>
       </listitem>
     </itemizedlist>
@@ -35,8 +49,19 @@
     <itemizedlist spacing="compact">
       <listitem>
         <para>
-          Please remove this line when you add the first item since
-          docbook requires the section to be non-empty
+          The <literal>isCompatible</literal> predicate checking CPU
+          compatibility is no longer exposed by the platform sets
+          generated using <literal>lib.systems.elaborate</literal>. In
+          most cases you will want to use the new
+          <literal>canExecute</literal> predicate instead which also
+          considers the kernel / syscall interface. It is briefly
+          described in the release’s
+          <link linkend="sec-release-22.11-highlights">highlights
+          section</link>.
+          <literal>lib.systems.parse.isCompatible</literal> still
+          exists, but has changed semantically: Architectures with
+          differing endianness modes are <emphasis>no longer considered
+          compatible</emphasis>.
         </para>
       </listitem>
     </itemizedlist>
diff --git a/nixos/doc/manual/release-notes/rl-2211.section.md b/nixos/doc/manual/release-notes/rl-2211.section.md
index a795c09dcf1..6dec063f403 100644
--- a/nixos/doc/manual/release-notes/rl-2211.section.md
+++ b/nixos/doc/manual/release-notes/rl-2211.section.md
@@ -6,7 +6,16 @@ Support is planned until the end of June 2023, handing over to 23.05.
 
 In addition to numerous new and upgraded packages, this release has the following highlights:
 
-- Please remove this line when you add the first item since docbook requires the section to be non-empty
+- During cross-compilation, tests are now executed if the test suite can be executed
+  by the build platform. This is the case when doing “native” cross-compilation
+  where the build and host platforms are largely the same, but the nixpkgs' cross
+  compilation infrastructure is used, e.g. `pkgsStatic` and `pkgsLLVM`. Another
+  possibility is that the build platform is a superset of the host platform, e.g. when
+  cross-compiling from `x86_64-unknown-linux` to `i686-unknown-linux`.
+  The predicate gating test suite execution is the newly added `canExecute`
+  predicate: You can e.g. check if `stdenv.buildPlatform` can execute binaries
+  built for `stdenv.hostPlatform` (i.e. produced by `stdenv.cc`) by evaluating
+  `stdenv.buildPlatform.canExecute stdenv.hostPlatform`.
 
 <!-- To avoid merge conflicts, consider adding your item at an arbitrary place in the list instead. -->
 
@@ -18,7 +27,14 @@ In addition to numerous new and upgraded packages, this release has the followin
 
 ## Backward Incompatibilities {#sec-release-22.11-incompatibilities}
 
-- Please remove this line when you add the first item since docbook requires the section to be non-empty
+- The `isCompatible` predicate checking CPU compatibility is no longer exposed
+  by the platform sets generated using `lib.systems.elaborate`. In most cases
+  you will want to use the new `canExecute` predicate instead which also
+  considers the kernel / syscall interface. It is briefly described in the
+  release's [highlights section](#sec-release-22.11-highlights).
+  `lib.systems.parse.isCompatible` still exists, but has changed semantically:
+  Architectures with differing endianness modes are *no longer considered compatible*.
+
 <!-- To avoid merge conflicts, consider adding your item at an arbitrary place in the list instead. -->
 
 ## Other Notable Changes {#sec-release-22.11-notable-changes}
diff --git a/pkgs/development/libraries/capnproto/default.nix b/pkgs/development/libraries/capnproto/default.nix
index 75b5f14d67c..aeb9728af82 100644
--- a/pkgs/development/libraries/capnproto/default.nix
+++ b/pkgs/development/libraries/capnproto/default.nix
@@ -17,9 +17,9 @@ stdenv.mkDerivation rec {
   };
 
   nativeBuildInputs = [ cmake ]
-    ++ lib.optional (!(stdenv.hostPlatform.isCompatible stdenv.buildPlatform)) capnproto;
+    ++ lib.optional (!(stdenv.buildPlatform.canExecute stdenv.hostPlatform)) capnproto;
 
-  cmakeFlags = lib.optional (!(stdenv.hostPlatform.isCompatible stdenv.buildPlatform)) "-DEXTERNAL_CAPNP";
+  cmakeFlags = lib.optional (!(stdenv.buildPlatform.canExecute stdenv.hostPlatform)) "-DEXTERNAL_CAPNP";
 
   # Upstream 77ac9154440bcc216fda1092fd5bb51da62ae09c, modified to apply to v0.9.1.  Drop on update.
   patches = lib.optional stdenv.hostPlatform.isMusl ./musl-no-fibers.patch;
diff --git a/pkgs/development/libraries/libffi/default.nix b/pkgs/development/libraries/libffi/default.nix
index 6a22d585fbc..125beae01ef 100644
--- a/pkgs/development/libraries/libffi/default.nix
+++ b/pkgs/development/libraries/libffi/default.nix
@@ -1,7 +1,9 @@
 { lib, stdenv, fetchurl, fetchpatch
 , autoreconfHook
 
-, doCheck ? true # test suite depends on dejagnu which cannot be used during bootstrapping
+  # test suite depends on dejagnu which cannot be used during bootstrapping
+  # dejagnu also requires tcl which can't be built statically at the moment
+, doCheck ? !(stdenv.hostPlatform.isStatic)
 , dejagnu
 }:
 
diff --git a/pkgs/stdenv/generic/make-derivation.nix b/pkgs/stdenv/generic/make-derivation.nix
index ed457019c55..395c1586a26 100644
--- a/pkgs/stdenv/generic/make-derivation.nix
+++ b/pkgs/stdenv/generic/make-derivation.nix
@@ -167,8 +167,8 @@ makeOverlayable (overrideAttrs:
 let
   # TODO(@oxij, @Ericson2314): This is here to keep the old semantics, remove when
   # no package has `doCheck = true`.
-  doCheck' = doCheck && stdenv.hostPlatform == stdenv.buildPlatform;
-  doInstallCheck' = doInstallCheck && stdenv.hostPlatform == stdenv.buildPlatform;
+  doCheck' = doCheck && stdenv.buildPlatform.canExecute stdenv.hostPlatform;
+  doInstallCheck' = doInstallCheck && stdenv.buildPlatform.canExecute stdenv.hostPlatform;
 
   separateDebugInfo' = separateDebugInfo && stdenv.hostPlatform.isLinux && !(stdenv.hostPlatform.useLLVM or false);
   outputs' = outputs ++ lib.optional separateDebugInfo' "debug";
diff --git a/pkgs/stdenv/linux/default.nix b/pkgs/stdenv/linux/default.nix
index 5c5ca64b1e9..ace0d704b72 100644
--- a/pkgs/stdenv/linux/default.nix
+++ b/pkgs/stdenv/linux/default.nix
@@ -31,7 +31,7 @@
   # compatible with or current architecture.
   getCompatibleTools = lib.foldl (v: system:
     if v != null then v
-    else if localSystem.isCompatible (lib.systems.elaborate { inherit system; }) then archLookupTable.${system}
+    else if localSystem.canExecute (lib.systems.elaborate { inherit system; }) then archLookupTable.${system}
     else null) null (lib.attrNames archLookupTable);
 
   archLookupTable = table.${localSystem.libc}