diff --git a/sipbuild/project.py b/sipbuild/project.py
--- a/sipbuild/project.py
+++ b/sipbuild/project.py
@@ -336,13 +336,13 @@ class Project(AbstractProject, Configurable):
             # We expect a two part tag so leave anything else unchanged.
             parts = platform_tag.split('-')
             if len(parts) == 2:
-                if self.minimum_glibc_version > (2, 17):
+                if self.minimum_glibc_version > (2, 17) or parts[1] not in {"x86_64", "i686", "aarch64", "armv7l", "ppc64", "ppc64le", "s390x"}:
                     # PEP 600.
                     parts[0] = 'manylinux'
                     parts.insert(1,
                             '{}.{}'.format(self.minimum_glibc_version[0],
                                     self.minimum_glibc_version[1]))
-                elif self.minimum_glibc_version > (2, 12):
+                elif self.minimum_glibc_version > (2, 12) or parts[1] not in {"x86_64", "i686"}:
                     # PEP 599.
                     parts[0] = 'manylinux2014'
                 elif self.minimum_glibc_version > (2, 5):