--- a/m4/ax_boost_base.m4
+++ b/m4/ax_boost_base.m4
@@ -33,7 +33,7 @@
 #   and this notice are preserved. This file is offered as-is, without any
 #   warranty.
 
-#serial 20
+#serial 22
 
 AC_DEFUN([AX_BOOST_BASE],
 [
@@ -91,9 +91,17 @@ if test "x$want_boost" = "xyes"; then
     dnl are found, e.g. when only header-only libraries are installed!
     libsubdirs="lib"
     ax_arch=`uname -m`
-    if test $ax_arch = x86_64 -o $ax_arch = ppc64 -o $ax_arch = s390x -o $ax_arch = sparc64; then
+    case $ax_arch in
+      x86_64|ppc64|s390x|sparc64|aarch64)
         libsubdirs="lib64 lib lib64"
-    fi
+        ;;
+    esac
+
+    dnl allow for real multi-arch paths e.g. /usr/lib/x86_64-linux-gnu. Give
+    dnl them priority over the other paths since, if libs are found there, they
+    dnl are almost assuredly the ones desired.
+    AC_REQUIRE([AC_CANONICAL_HOST])
+    libsubdirs="lib/${host_cpu}-${host_os} $libsubdirs"
 
     dnl first we check the system location for boost libraries
     dnl this location ist chosen if boost libraries are installed with the --layout=system option