I'm not sure I see the complication. Graham (nid player) and I make a team. Graham is stuck with his loan self, cuz everyone hates bugs, and I (cuz, y'know, imperial is better) can add in most things.
Everything else is exactly the same. If I had any battle brothers, they would be battle brothers to me, not Graham. Allies of convenience are pretty much how doubles treat each others armies anyway. "unholy alliance", if say, I picked DE, would presumably only apply to me as well.
For extra fun, if you wanted, you could apply the matrix between teams, treating "can't ally" as the unholy alliance. I don't think this represents any extra book keeping for Sam, as I'm sure one's opponents will be more than willing to enforce it.
But I don't really recommend that, cuz frankly, tyranid players have had a bad enough run of it. People will want to know why tyrnaids can be on any team with anybody at all, yadda yadda, and besides, I'm selfish, my main bud plains tyranids.