diff --git a/Makefile b/Makefile
index 8d15526c2..f54ebe8d2 100644
--- a/Makefile
+++ b/Makefile
@@ -317,6 +317,11 @@ ifeq ($(PLATFORM),darwin)
   BASE_CFLAGS += -mmacosx-version-min=$(MACOSX_VERSION_MIN) \
                  -DMAC_OS_X_VERSION_MIN_REQUIRED=$(MAC_OS_X_VERSION_MIN_REQUIRED)
 
+  MACOSX_ARCH=$(ARCH)
+  ifeq ($(ARCH),x86)
+    MACOSX_ARCH=i386
+  endif
+
   ifeq ($(ARCH),ppc)
     BASE_CFLAGS += -arch ppc
     ALTIVEC_CFLAGS = -faltivec
@@ -348,15 +353,31 @@ ifeq ($(PLATFORM),darwin)
   endif
 
   ifeq ($(CROSS_COMPILING),1)
-    ifeq ($(ARCH),x86_64)
-      CC=x86_64-apple-darwin13-cc
-      RANLIB=x86_64-apple-darwin13-ranlib
-    else
-      ifeq ($(ARCH),x86)
-        CC=i386-apple-darwin13-cc
-        RANLIB=i386-apple-darwin13-ranlib
-      else
-        $(error Architecture $(ARCH) is not supported when cross compiling)
+    # If CC is already set to something generic, we probably want to use
+    # something more specific
+    ifneq ($(findstring $(strip $(CC)),cc gcc),)
+      CC=
+    endif
+
+    ifndef CC
+      ifndef DARWIN
+        # macOS 10.9 SDK
+        DARWIN=13
+        ifneq ($(findstring $(ARCH),ppc ppc64),)
+          # macOS 10.5 SDK, though as of writing osxcross doesn't support ppc/ppc64
+          DARWIN=9
+        endif
+        ifeq ($(ARCH),arm64)
+          # macOS 11.3 SDK
+          DARWIN=20.4
+        endif
+      endif
+
+      CC=$(MACOSX_ARCH)-apple-darwin$(DARWIN)-cc
+      RANLIB=$(MACOSX_ARCH)-apple-darwin$(DARWIN)-ranlib
+
+      ifeq ($(call bin_path, $(CC)),)
+        $(error Unable to find osxcross $(CC))
       endif
     endif
   endif