You would be much better getting a large USB drive.. archiving the current material to that drive and erase and start over on the TC.
If the TC is out of warranty.. open it up and put a 3TB or 4TB drive in it yourself.
You can move old backups if you really want to.. but 2TB to 3TB is not going to last long,, and the actual transfer will take ages.. make sure you have them connected by gigabit.. and a computer with gigabit.. it has to transfer TC1---Computer---TC2.
The USB drive sounds like a good idea. The upgrade of the TC to 4TB also interesting as I didn't know it was possible. Presumably then the TC itself is a harde drive with some type of wireless network capability?
The TC is an airport extreme with a hard disk inside.
Rather than a hard disk with wireless.
Opening and changing hard drive.