Allow us to create our own whole party of characters, vicariously through multiplayer and setting it to private settings? You used to be able to for 1 and 2 so I keep an eye out for a version that still does that.

AFAIK, no. In singleplayer, most of your party members will be pre-written characters or semi-generic pets and summons. I don't know about multiplayer, but it might be possible there.

Your party is based on the difficulty you are in. You basically get one party member + one pet for normal, 2 party members + 1 pet for nightmare, and iirc 3 party members + 1 pet for the equivalent of Hell.

There are ways to unlock it, and the inn keeper in the first town as I recall, allows you to set up custom party members. It might be tied into the software that unlocks the full party, but I'm not sure.

Back in the day, I tinkered around with it on an unofficial patch. Can't remember the name, sorry.