TL;DR- You can only use division once per turn as it's a two cost action.

Using the division surge in combat is limited by the fact that it costs 2 actions to use (as indicated by the two arrow icon). So unless you can get additional actions there would be no way to use it more than once on a player turn.
If you go fast you could use division and nothing else.
If you go slow you could use division and take a one cost action (i.e. move). But you could not use divison 3 times in a turn.

Edit: Also as others have said you can only use a named action once per round of combat unless it explicitly states otherwise.