So, do you mean that all these partners are involved with each other intimately, or that only one of them is? Either way, thorny problem, indeed. Patience to see what happens next is needed; sometimes just waiting and watching partner's drama unfold can help them come to their senses (since they don't feel so much pressure to act any way other than they normally would). Expressing concern over the situation usually works out well for me, but sometimes a bit more is required to get the trouble out of my face, such as saying "Fuck this shit; get your priorities together."
Really, it's all about reactions. Just because one person does something bone-headed doesn't mean another has to respond by acting nutty, too. Cool-headedness goes a long way, and often a simple statement showing them that their behavior toward each other is less than mature can make all the difference. I've seen marriages break up over this stuff, so anyone in a situation where partners don't get along should tread lightly.
Unless I totally misunderstood the situation...

I would solicit specific concerns and objections and take them into account, but I don't issue vetoes and I've never been subjected to one. There might be ways to reduce their impact on each other short of pretending the other doesn't exist. Don't force them to get together after a few good-faith efforts to connect prove they're oil and water. Talking everything out in a big huggy circle just isn't going to happen for some people, at best it's only going to produce insincere short-term healing over of abscesses.

I have told a partner that I just flat out could not be friends with their other lover and not to pressure me to have any contact with that person - no more than is strictly necessary. I feel some guilt over that but efforts to establish an active friendship (or even socialize cordially) were backfiring nastily, and bringing out the worst in me. It's a liveable compromise for now.

I have have to ask. Is "crazy" a euphemism for "Making things difficult for Edward?"

I've been revisiting this topic lately.

I think my head is wrapping around the idea of using analogies.

If I had a partner with a horrible disease, that would suck, and I have to decide how much effort I want to put into helping with their comfort, but I don't HAVE the disease.

If I have a partner that has an annoying habit, I have to decide to either put up with it, or try to change them. If they want to change anyway, great, but otherwise, it's just gonna hurt trying.