diff --git a/var/spack/repos/builtin/packages/amdlibflame/package.py b/var/spack/repos/builtin/packages/amdlibflame/package.py
index d8e06c6b43..e1b96e042e 100644
--- a/var/spack/repos/builtin/packages/amdlibflame/package.py
+++ b/var/spack/repos/builtin/packages/amdlibflame/package.py
@@ -59,10 +59,11 @@ class Amdlibflame(LibflameBase):
 
     conflicts("+ilp64", when="@:3.0.0", msg="ILP64 is supported from 3.0.1 onwards")
     conflicts("threads=pthreads", msg="pthread is not supported")
-    conflicts("threads=openmp", msg="openmp is not supported")
+    conflicts("threads=openmp", when="@:3", msg="openmp is not supported by amdlibflame < 4.0")
 
     patch("aocc-2.2.0.patch", when="@:2", level=1)
     patch("cray-compiler-wrapper.patch", when="@:3.0.0", level=1)
+    patch("supermat.patch", when="@4.0:4.1", level=1)
 
     provides("flame@5.2", when="@2:")
 
@@ -109,13 +110,13 @@ def configure_args(self):
             )
 
         # From 3.2 version, amd optimized flags are encapsulated under:
-        # enable-amd-flags for gcc compiler
-        # enable-amd-aocc-flags for aocc compiler
+        # enable-amd-aocc-flags for AOCC compiler
+        # enable-amd-flags for all other compilers
         if "@3.2:" in self.spec:
-            if "%gcc" in self.spec:
-                args.append("--enable-amd-flags")
             if "%aocc" in self.spec:
                 args.append("--enable-amd-aocc-flags")
+            else:
+                args.append("--enable-amd-flags")
 
         if "@:3.1" in self.spec:
             args.append("--enable-external-lapack-interfaces")
diff --git a/var/spack/repos/builtin/packages/amdlibflame/supermat.patch b/var/spack/repos/builtin/packages/amdlibflame/supermat.patch
new file mode 100644
index 0000000000..374ffa3dc3
--- /dev/null
+++ b/var/spack/repos/builtin/packages/amdlibflame/supermat.patch
@@ -0,0 +1,11 @@
+diff --git a/src/map/lapack2flamec/FLA_getrf.c b/src/map/lapack2flamec/FLA_getrf.c
+index af70857e..1ffc63a1 100644
+--- a/src/map/lapack2flamec/FLA_getrf.c
++++ b/src/map/lapack2flamec/FLA_getrf.c
+@@ -232,6 +232,7 @@ extern fla_context global_context;
+ 
+ #else /* FLA_ENABLE_SUPERMATRIX */
+ 
++#define LAPACK_getrf_body_s LAPACK_getrf_body
+ #define LAPACK_getrf_body_d LAPACK_getrf_body
+ #define LAPACK_getrf_body_z LAPACK_getrf_body