New to Knights, question about lore.

I got a couple Knight Armigers over the holidays that I want to run with my 30k and 40k Night Lords, and 40k Dark Angels. I am pretty new to the lore and am learning more about houses and freeblades. Would there be any reason for a house to work with both traitors and loyalists? Could there reasonably be a group of common-minded freeblades that would be willing to work together as a mercenary group? I think I may homebrew a house or merc group so I can field these knights in a way that the lore would make sense.