6th Gen Professor Birch will give you Johto, Sinnoh and Unova starters.

Besides giving you a Hoenn Starter at the beginning of the game, Professor Birch will give you a Johto, Sinnoh and Unova starter Pokemon as well. In order to get the Johto ones, all you need to do is enter the Hall of Fame once. After completing the Delta Episode, you can get a Unova starter, and after entering the hall of fame a second time, you can obtain a Sinnoh starter.

Which starters did you pick from Professor Birch on the subsequent times he gave you one?

In my quest for starters:

First playthrough of Omega Ruby: Torchic, Totodile, Oshawott, Piplup
Second playthough of Omega Ruby: Mudkip, Cyndaquil, Tepig, Chimchar
Third time: The missing grass ones :P

I was going to do a mono-green run the third time, but it didn't work out so whatever.

Then they all went to Pokemon Ultra Moon never to be used again. The end.