I feel like if everyone was in agreement about the situation, it would be doable.
But as with the nature of Chaos, if someone doesn't like it, they're not gonna let it happen. Then you get into the semantics of "can I do this without the other party's permission," and that's always a resounding no.
The stipulation on SSDs is "only a major faction can field one," and "you have to complete three dominions in a month." So, if'n you did that, I don't see why the other hoops being jumped through would stop you from having one.