Comment by mananaysiempre

Depending on the effort you’re willing to put in, you don’t have to: gzip has a specific provision for concatenated files and tar is a flat array of (file) records each followed by file data, terminated by a sentinel record, so what you need to do is to trim the sentinel off the first tar.gz and then append the second one as is. I don’t know of a ready-made tool that would be able to chop off a gzip file’s last 512 uncompressed bytes without recompressing it in full, but it ought to be possible.