Not sure if this has been suggested before because I haven't read the entire thread but I seem to remember hearing that part of the difficulty of having >4 in the party would be due to the complexity of inter party interactions with the characters. It seems that this could be reduced by having 2 types of companions. Tier 1 companions are what we see them as now. Banter between themselves, conflicts, camp dialogs, etc.
However if they allowed more than 4, the remaining could be Tier 2 companions more akin to what we see as familiars now. No dialogs, no interaction with NPC's, etc. because they're just part of the muscle, not part of the main party really.
So really just good for expanding combat situations.