diff --git a/peps/pep-0803.rst b/peps/pep-0803.rst
index c44cf0b78f6..ef056591300 100644
--- a/peps/pep-0803.rst
+++ b/peps/pep-0803.rst
@@ -288,6 +288,20 @@ The tag ``abi3t`` is chosen to reflect the fact that this ABI is similar to
 uses the letter ``t`` in existing, version-specific ABI tags like ``cp314t``).
 
 
+Filename tag
+------------
+
+On systems that use the ``abi3`` tag in filenames, a new filename tag
+(``abi3t``) is added so that older stable ABI extensions
+(:samp:`{name}.abi3.so`) can be installed in the same directory as ones that
+support Stable ABI for free-threaded Python (:samp:`{name}.abi3t.so`).
+
+There can only be one ABI tag in a filename (there is no concept of "compressed
+tag sets like in wheel tags), so extensions that are compatible with both ABIs
+at once need to use *one* of the tags -- the new one (``abi3t``), which
+is currently unused.
+
+
 Specification
 =============
 
@@ -461,14 +475,34 @@ and may be removed in future CPython versions,
 if the internal object layout needs to change.
 
 
-The ``abi3t`` wheel tag
------------------------
+The ``abi3t`` wheel and filename tags
+-------------------------------------
 
 Wheels that use a stable ABI compatible with free-threading CPython builds
 should use a new `ABI tag`_: ``abi3t``.
 
 .. _ABI tag: https://packaging.python.org/en/latest/specifications/platform-compatibility-tags/#abi-tag
 
+On systems where filenames of Stable ABI extensions end with ``.abi3.so``,
+extensions that support free-threading should instead use ``abi3t.so``.
+This includes extensions compatible with *both* ``abi3`` and ``abi3t``.
+
+On these systems, all builds of CPython -- GIL-enabled and free-threaded --
+will load extensions with the ``abi3t`` tag.
+Free-threaded builds will -- unlike in 3.14 -- *not* load extensions
+with the ``abi3`` tag.
+If files are present with both tags, GIL-enabled builds will prefer
+"their" ``*.abi3.so`` over ``*.abi3t.so``.
+
+Put another way, ``importlib.machinery.EXTENSION_SUFFIXES`` will be
+(for ``x86_64-linux-gnu`` builds of CPython):
+
+* ``python3.15``:
+  ``['.cpython-315-x86_64-linux-gnu.so', '.abi3.so', '.abi3t.so', '.so']``
+* ``python3.15t``:
+  ``['.cpython-315-x86_64-linux-gnu.so', '.abi3t.so', '.so']``
+
+
 Recommendations for installers
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
@@ -504,6 +538,13 @@ In the above, :samp:`{v}` stands for a the lowest Python version with which
 the extension should be compatible, in :c:func:`Py_PACK_VERSION` format.
 In the cases above, this version must be set to 3.15 or higher.
 
+In both cases, if a resulting extension's *filename* would use the ``abi3``
+tag (that is, :samp:`{modulename}.abi3.so` on Linux, macOS, and similar),
+the ``abi3t`` tag should be used instead (that is,
+:samp:`{modulename}.abi3t.so` on those systems).
+If this tag is not used, there should be no change. (This is always the case
+on Windows, where the filename should remain :samp:`{name}.pyd`.)
+
 .. _compressed tag set: https://packaging.python.org/en/latest/specifications/platform-compatibility-tags/#compressed-tag-sets
 
 The version of the Stable ABI, both ``abi3`` and ``abi3t``, is indicated by
@@ -783,15 +824,8 @@ Naming this ``abi4``
 Instead of ``abi3t``, we could “bump the version” and use ``abi4`` instead.
 The difference is largely cosmetic.
 
-However, one thing this PEP does not propose is changing the *filename*
-tag: extensions will be named with the extensions like ``.abi3.so``.
-Changing this while keeping compatibility with GIL-enabled builds would be
-an unnecessary technical change.
-
-Using ``abi3.abi4`` in wheel tags but only ``.abi3`` in filenames would
-look more inconsistent than ``abi3.abi3t`` and ``.abi3``.
-
-If we added an ``abi4`` tag, the ``Py_LIMITED_API`` value would either need to:
+If we added an ``abi4`` tag, the value of the opt-in macro (``Py_TARGET_ABI4``
+or ``Py_LIMITED_API`` or some such)  would either need to:
 
 * change to start with ``4`` to match ``abi4``, but no longer correspond
   to ``PY_VERSION_HEX`` (making it harder to generate and check), or