Okay, let me tell you why I reject your contribution at this point.

The patch you submitted may be well-suited for your purposes but it does not meet the requirements of a standard library implementation because it is not generic and comprehensive enough.

It contains duplicate code, spelling mistakes and needless code changes e.g.  in test_tarfile.py.

It does not expose one set of volumes as one tar archive to the user. It is not possible to iterate over all members of all volumes in one go. It does not allow random-access.

Actually, it does not implement complete multivolume support but only the "easy" parts.  For example, it fails to read GNU tar archives that are split in the middle of a pax header block sequence. The other way around, when writing it makes a split only when it is inside the data part of a member. Hence, it is possible that a volume turns out smaller than max_volume_size which is not only inaccurate but also bad on a tape device.

If you decide that you still want multivolume support in tarfile, feel free to reopen this issue with a new and significantly better patch. I gave you a number of clues on what I think is required.