It's possible, but completely pointless.
Just change the name of the segment.
One of the selling points to the "Go back to Booking Screen" feature was put into the game, besides the benefit of fixing mistakes or changing stuff, was that you could do something like the three faces or Foley. But it's pointless to do something like that because you'd just be changing to an alter ego, which doesn't at all matter in the game, and maybe changing the name of the gimmick, which matters even less.
Also I don't believe you could be able to do a a battle royal where the same person appears multiple times.