diff --git a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS.cmake b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS.cmake
index 9093426ccc..ff665e97f6 100644
--- a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS.cmake
+++ b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS.cmake
@@ -23,6 +23,38 @@ if ( NOT DEFINED ALLOW_64BIT_BLAS )
     set ( ALLOW_64BIT_BLAS false )
 endif ( )
 
+#-------------------------------------------------------------------------------
+# look for a specific BLAS library
+#-------------------------------------------------------------------------------
+
+# To request specific BLAS, use either (for example):
+#
+#   CMAKE_OPTIONS="-DBLA_VENDOR=Apple" make
+#   cd build ; cmake -DBLA_VENDOR=Apple .. ; make
+#
+# Note that the ALLOW_64BIT_BLAS flag is ignored in this case.  If you want
+# to select a specific BLAS integer size, use -DBLA_SIZEOF_INTEGER=64 or 32.
+
+if ( DEFINED BLA_VENDOR )
+    # only look for the BLAS from a single vendor
+    message ( STATUS "============================================" )
+    message ( STATUS "Looking for BLAS: "  ${BLA_VENDOR} )
+    if ( NOT DEFINED BLA_SIZEOF_INTEGER )
+        message ( FATAL_ERROR "Both BLA_VENDOR and BLA_SIZEOF_INTEGER must be specified" )
+    endif ( )
+    # only look for the BLAS with a specific integer size
+    find_package ( BLAS REQUIRED )
+    find_package ( LAPACK REQUIRED )
+    if ( BLA_SIZEOF_INTEGER EQUAL 8 )
+        include ( SuiteSparseBLAS64 )
+    elseif ( BLA_SIZEOF_INTEGER EQUAL 4 )
+        include ( SuiteSparseBLAS32 )
+    else ( )
+        message ( FATAL_ERROR "BLA_SIZEOF_INTEGER invalid (must be 4 or 8)" )
+    endif ( )
+    return ( )
+endif ( )
+
 #-------------------------------------------------------------------------------
 # these blocks of code can be rearranged to change the search order for the BLAS
 #-------------------------------------------------------------------------------
@@ -35,7 +67,6 @@ if ( ALLOW_64BIT_BLAS )
     find_package ( BLAS )
     find_package ( LAPACK )
     if ( BLAS_FOUND AND LAPACK_FOUND )
-        add_compile_definitions ( BLAS_INTEL_64ILP )
         include ( SuiteSparseBLAS64 )
         return ( )
     endif ( )
@@ -48,7 +79,6 @@ set ( BLA_SIZEOF_INTEGER 4 )
 find_package ( BLAS )
 find_package ( LAPACK )
 if ( BLAS_FOUND AND LAPACK_FOUND )
-    add_compile_definitions ( BLAS_INTEL_64LP )
     include ( SuiteSparseBLAS32 )
     return ( )
 endif ( )
@@ -60,7 +90,6 @@ set ( BLA_SIZEOF_INTEGER 4 )
 find_package ( BLAS )
 find_package ( LAPACK )
 if ( BLAS_FOUND AND LAPACK_FOUND )
-    add_compile_definitions ( BLAS_APPLE )
     include ( SuiteSparseBLAS32 )
     return ( )
 endif ( )
@@ -73,7 +102,6 @@ if ( ALLOW_64BIT_BLAS )
     find_package ( BLAS )
     find_package ( LAPACK )
     if ( BLAS_FOUND AND LAPACK_FOUND )
-        add_compile_definitions ( BLAS_ARM_MP )
         include ( SuiteSparseBLAS64 )
         return ( )
     endif ( )
@@ -86,7 +114,6 @@ set ( BLA_SIZEOF_INTEGER 4 )
 find_package ( BLAS )
 find_package ( LAPACK )
 if ( BLAS_FOUND AND LAPACK_FOUND )
-    add_compile_definitions ( BLAS_ARM_ILP64_MP )
     include ( SuiteSparseBLAS32 )
     return ( )
 endif ( )
@@ -99,7 +126,6 @@ if ( ALLOW_64BIT_BLAS )
     find_package ( BLAS )
     find_package ( LAPACK )
     if ( BLAS_FOUND AND LAPACK_FOUND )
-        add_compile_definitions ( BLAS_IBMESSL_SMP_64 )
         include ( SuiteSparseBLAS64 )
         return ( )
     endif ( )
@@ -112,7 +138,6 @@ set ( BLA_SIZEOF_INTEGER 4 )
 find_package ( BLAS )
 find_package ( LAPACK )
 if ( BLAS_FOUND AND LAPACK_FOUND )
-    add_compile_definitions ( BLAS_IBMESSL_SMP_32 )
     include ( SuiteSparseBLAS32 )
     return ( )
 endif ( )
@@ -125,7 +150,6 @@ if ( ALLOW_64BIT_BLAS )
     find_package ( BLAS )
     find_package ( LAPACK )
     if ( BLAS_FOUND AND LAPACK_FOUND )
-        add_compile_definitions ( BLAS_OPENBLAS_64 )
         include ( SuiteSparseBLAS64 )
         return ( )
     endif ( )
@@ -138,7 +162,6 @@ set ( BLA_SIZEOF_INTEGER 4 )
 find_package ( BLAS )
 find_package ( LAPACK )
 if ( BLAS_FOUND AND LAPACK_FOUND )
-    add_compile_definitions ( BLAS_OPENBLAS )
     include ( SuiteSparseBLAS32 )
     return ( )
 endif ( )
diff --git a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS32.cmake b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS32.cmake
index d746070ae8..71b3e04001 100644
--- a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS32.cmake
+++ b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS32.cmake
@@ -10,6 +10,7 @@
 
 # actions taken when a 32-bit BLAS has been found
 
-message ( STATUS "Found 32-bit BLAS+LAPACK" )
+message ( STATUS "Found ${BLA_VENDOR} 32-bit BLAS+LAPACK" )
+add_compile_definitions ( BLAS_${BLA_VENDOR} )
 set ( SuiteSparse_BLAS_integer "int32_t" )
 
diff --git a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS64.cmake b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS64.cmake
index f5710f6bcf..eefab62c0f 100644
--- a/SuiteSparse_config/cmake_modules/SuiteSparseBLAS64.cmake
+++ b/SuiteSparse_config/cmake_modules/SuiteSparseBLAS64.cmake
@@ -10,7 +10,8 @@
 
 # actions taken when a 64-bit BLAS has been found
 
-message ( STATUS "Found 64-bit BLAS+LAPACK" )
+message ( STATUS "Found ${BLA_VENDOR} 64-bit BLAS+LAPACK" )
+add_compile_definitions ( BLAS_${BLA_VENDOR} )
 add_compile_definitions ( BLAS64 )
 set ( SuiteSparse_BLAS_integer "int64_t" )