When other countries historically have ‘solved’ this problem, it ends up being pretty terrible for the minority groups who either have their land seized when they get displaced or get wholesale slaughtered (see partition when India and Pakistan were formed, Bosnia/Herzegovina and the Balkans War, Rwandan genocide, or the active issues in Israel), and in Lebanon EVERYONE is a minority group [https://en.m.wikipedia.org/wiki/Demographics_of_Lebanon#Reli...].
And if you’re going to say ‘Hey, but Muslims have 60%!’, the current Muslim group are roughly 50/50 Sunni and Shia, which have similar history as Catholics and Protestants - aka they hate each other and have a history of bloody fights. That means each group is actually smaller than the Christians as a whole (who are more like 35-45%), but also larger than any one Christian Sect (which includes said Catholics and Protestants BTw).
So for the most part since no one has enough of a majority to assert who belongs where (and it certainly isn’t obvious to everyone else either) or who would be naturally ‘in charge’, it’s endless jockeying for position, extremist recruiting within their groups, corruption to benefit their minority group and screw over the others behind everyone’s back, and the occasional terrorist bombing.
Fun times eh?