At first, I'd like to take back my comment on this patch being too complex for too little benefit. That is no real argument.

Okay, I gave it a shot and I have a few more remarks:

The patch does not support iterating over a multi-volume tar archive, e.g. for TarFile.list(). You must implement this.

In my opinion, a tar archive is one logical unit even if it spans across multiple volumes. Thus, it is vital to have .getmembers() and .getnames() reflect the entirety of the archive, e.g. to support "if filename in .getnames()". I think it could be a good idea to store the volume number along each TarInfo object for random-access.

By the way, which standard are you referring to? The only one I know of is POSIX pax which doesn't say anything about multiple volumes.