I am rather sure that you can make a copy from the "old" TM backup to the "new" TM backup disk and then use that. The problem with this is that you first have to convince TM that it has to accept the new UIDD of the new disk for adding to the old backup. I am pretty sure that you can do that (pondini.org). I did it, because I wanted to preserve older times too.
I will never do it again, making sure that I make backups without deleting older files that I want to conserve.
But I argue with the others that it is MUCH easier to start a new backup on a new disk. It costs less time to make a brand new TM backup, than finding out how to do what I said above.
BTW: I think TM is the most brilliant backup system there is. I use disks that are at least 3x the startup disk size.
Lex.