Can I play DD on both gen XBox consoles?

[lckdb_XBL]

I have a preorder version of the game on old gen hooked up to my living room TV. Hitting in offline is fine but it is clear that it isn’t workable in most H2H games…I’m struggling to stay above the Mendoza line because I can’t pick up the pitches.

Thinking about getting a Series X and hooking it up to my monitor which is for gaming. Can I have both consoles active with MLB the Show so that my kids can play on the old gen and I don’t lose my DD team on Series X?

Thanks!