This is a good question!
I don't know if interactions between specific slaves is controllable. I've been able to get them all to be neutral, friendly or affectionate with each other, though. That I'm guessing should mostly be credited to assigning an appropriate Headgirl (headperson). It's a job that's only available to slaves of Rich level or above, and only available after you own 8 or more slaves. The appropriate "Headgirl Setting" in "Mansion Settings" should be used. I used a slave with max charm and the Patronage setting.
I'm sure it also helps if your communal space isn't overcrowded and there are sufficient luxuries for all, but that too is speculation.