...or talk to them, or have coffee/dinner/drinks with them. You need their permission--period.
Really, that is it. Granted, we do have strict rules about STI testing, but if the conditions of our relationship are met, and all appropriate consents are in place, my partners can can have sex with whomever they like. They can also kiss whomever they like, play with whomever they like, and generally spend time with whomever they like (all three of which are much more likely to happen than actual sex!).
I have written in the past about how much it pisses me off when people ask my nesting partner for permission to do anything to my body, so it would be hypocritical of me to expect permission about his body and/or time to be asked of me.
Do we discuss time we are going to spend with others? Of course. Do we discuss any potential sex or any possible play outside of a party? Absolutely. But the reality is that we do not give each other "permission" in anything but the larger sense.
Do I want basic courtesy from anyone with whom he is involved? Yes, yes I do. They need to know I exist, and they need to be respectful of my time and relationship (just as I am respectful of theirs). But, they are not under any obligation to run anything past me.
He is the one who has to check with me, to make sure I am okay, to see if I have any reservations. He is in this relationship and so owes that to me as the other person in the relationship (as he owes it to anyone else he may be in a serious relationship with).
I generally feel the same way about anyone I am going to play with, though if their partner would like to talk to me first I certainly respect that. My basic feeling is that we are all adults, and I trust if someone is going to play with me they have whatever their version of permission is for said play.
I do tend to thank their partners after the play as a gesture of community and niceness and all-around good feeling, but, to me, that is not the same as asking for permission. That is acknowledging that another person shared their time and energy (in the form of their lover) with me, and the openness is appreciated.