LogFAQs > #979973229

The only non prio shift I can think of is the beginning of the main phase, which is considered an open game state.

https://yugipedia.com/wiki/Game_state

If it's open, the priority is on the turn player. The moment they declare anything that closes the game state, you can respond, and if you respond, you pass the prio to the other player

So technically you can respond like twice. When they declare the Main Phase end, you can respond, and when they declare battle phase and pass their activation, you can respond again at the beginning of the battle phase.