I am not an expert on mods or the GECK, but my understanding is a conflict will/can arise if two mods alter the same exact script, setting, item, etc. as another. Forcing load order of mods in this case can sometimes help, but not always.
So it's not how
many you have, it's what they change. If two companion mods both alter, say, Boonescipt, there will be a conflict and the first one that loads, its changes will work, but the 2nd one will/may not. I think most companion mods create their own scripts but do/may alter AI-Packages. If your companion mods are changing rules or textures for clothing meshes or something to that affect, perhaps that's one issue. I know the most recent version of Companion Sandbox caused certain clothes to turn "invisible" when worn by companions (I don't use/have FOOK), so I went back to an older version, because I'm too lazy to figure out why & maybe alter it myself.

Or another example, if I wanted to change a companion's stats for some reason and tried to make my own tiny mod for that, it might conflict with a companion mod or vice versa (load order again, too)...and in that case, I could make the stat changes
within the other mod - instead of making my own separate mod - and then it would all work.
Another possible reason for clothing mesh issues/mods is archive invalidation. This FO3 mod page explains it a bit (and the manual version seems to work in FNV w/a minor install change) http://www.fallout3nexus.com/downloads/file.php?id=944
But again, that's just how my inexpert self understands things based on reading and my own small experimentation...maybe someone knows more concrete details as well as an actual list of conflicting mods.