Pausing Other Relationships
When a dyad decides to "pause" another relationship outside of the dyad, it causes significant issues.
Is it ever okay when a dyad decides to pause one partner's outside relationship due to exploring their own relationship?
I think you need to put the responsibility where it lies. You're not dating the dyad. You're dating one person in that dyad who is not a captive of the other. They are a grown adult who is responsible for their own choices. The dyad has not decided to pause other relationships. That partner has decided that.
Now, they may be behaving cowardly and be blaming their partner for their own decisions. And maybe they do genuinely feel like they don't have a choice. But at the end of the day, they are the ones deciding to go along with this, even if it wasn't their idea and even if it's not something that they want for themselves. They are agreeing to it.
It's very easy to blame a metamour especially if we do have a partner that is blaming your metamour for their own decisions, but I would really encourage people to not allow anyone to get away with that. It doesn't really matter if it's "okay" for a dyad to do this. If this is not acceptable for you, then it's not acceptable. Even if it was something that other people were okay with, you don't actually have to be okay with it. You're allowed to set the terms of what you will and won't put up with.
However, if you're asking because you are part of that dyad, in general, I think that moves like this are not great. If you have to pause other relationships to focus on another one, it creates a "safe" space in closing that relationship that doesn't exist. Generally speaking, one would not break up with their partner to focus on their work. If you needed to stop your relationship to focus on your work, one would think there was a serious issue there that needed to be addressed. We understand if people get distracted by work and other things or have a big work project, but generally we expect people to be able to balance those multiple things in their lives.
The other issue is that a lot of relational problems need to solved while in relation and closing a relationship may be just delaying the inevitable. Consider how much time you are giving to one relationship vs. the others and figure out if both of you have the same idea of the amount of time you want to spend together vs with other people and see if you can come to some type of agreement or compromise rather than forcing other connections to close.
And if you decide to go forward with the idea that you will close your relationship with others if something goes "wrong", you should clearly communicate that to anyone who dates either of you so that they know that their relationship could be suddenly ended and they can decide if that is a risk they would like to take.
I hope this helps and good luck!