I feel it important to note that when we are talking about "guns for hire" factions, there is a great difference between the terms 'alliance' and 'business partnership'.
Another important thing is the reason of alliance. If faction A is allied with faction B for X reason, allied with faction C for Y reason but B and C are shooting at eachother for Z reason, and these reasons do not contradict eachother, the triangle can happily exist. Faction A can also share their technologies with B and C as long as the terms state that the two don't use tech from A against eachother, just to prevent A getting involved in conflict Z and needing to pick a side.
That's the beauty of Disco's diplomacy system, that it's not all black and white.