My first thought is that maybe the vicious blood-letting isn't really as rampant as the rumors suggest. Renaissance Italy is infamous for the in-fighting, blood feuds, and treachery within and between city states. But Italy didn't depopulate itself in a huge auto-genocidal bloodbath. I would propose that Drow society would have far more political and social maneuvering going on than outright murder and warfare. There is a lot of posturing, sabre-rattling, acts of brinkmanship, formal dueling, and so on. Rumors on the surface would, of course, paint the situation in lurid colors.
Yes, there is the occasional secret ambush or assassination, but open murder and blatant acts of war are rare. Being caught as a murderer of a house member gives rivals a convenient opportunity to band together to declare you traitor. Traitors are executed or exiled, possibly with all immediate family members, and their holdings divided up as rewards to the the "loyal" family members. Open warfare is rare as well. Each house has its strongholds and armed forces, but also vulnerable supply lines, trading routes, slave villages, mining operations, etc. which cannot be recklessly hazarded on a whim.
Now, having a Drow adventuring party presents other difficulties. If the members are from rival factions/houses then you need some plot devices to keep the party (mostly) outwardly focused. One obvious plot device is the "Greater Evil". The houses have formed a joint team (possibly one of a number of such teams) to counter something with threatens them all. Some quick ideas for the Greater Evil are:
- A dragon clan has gathered an army and is carving out a new empire
- Githyanki forces are making devastating raids from the ethereal plane at will; all are vulnerable
- Conquering Duergar wield new steampunk technology giving them a decisive edge on the battlefield
- Drow society is infiltrated by Cthulhu-style Elder God cultists, with a major summoning rumored soon
But I doubt I'll ever get to run it.