This is all looking really great. Is it possible to extend the rules for multiple players? (I realize that would mean adding balancing options, so probably not within the 7DRL, but could that work in principle?)
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The rules system would work very naturally for multiple players. The rules themselves are basically just miniatures skirmish rules, and they could be used to run any type of fantasy miniatures skirmish game.
The web app that generates the dungeon, of course, would generate dungeons expecting only one player is going through, but if you and a friend wanted to play, a simple tweak would be to just double the number of each monster that gets spawned into the room and double any treasures you find lying around the dungeon (as opposed to loot drops from enemies killed). Longer term, maybe the generator might generate dungeons for multiple heroes, but I'd consider it outside the scope of the 7DRL.
Another option would be to just hand-craft some adventures. The procgen adds the replayability, but there's no reason it couldn't be paired with handcrafted adventures for multiple people.
One potential issue using it with multiple players is the papercraft mini's themselves. The nice thing about the game being solitaire is that I was able to drastically reduce the amount of printing and assembly time by making the mini's only have to face one player, but if multiple players are going to be playing, that no longer applies. If that's the case, you'll probably want to print the mini's twice and "back" them so that they're presentable from the other direction. (The rules also work if you supply your own mini's, so if you've got mini's from playing D&D lying around, you can improvise easily. The rules even include instructions for gridless play if you are in the "rulers rather than squares" miniatures camp.)