If you can start at the same time if two, tag conversion to the new MP3 file will be available from the old MP3 files.
It is not possible to start two instances of MP3tag at the same time.
But: you can load the old and the new mp3-file at the same time and copy&paste all tags at once from one file to the other with the "Copy tag" function in the context menu of the files list.
You can even do that for more than one file at the same time if the source files and the target files are in the same sequence.
I would also like to have this feature.