How would you feel about Servant Interaction in-game?

Hi! So I was wondering what anyone thought about Servants interacting in battle. For example, if you have Gilgamesh and Saber Artoria in the same party in battle Gil could tease her and she could reply with annoyance or whatever she'd reply with. This would take place at a battles start and ending, I guess. Dunno, just something I thought could be neat. Thoughts?