2nd Quest Dungeons add seven new stair room possibilities - they are pictured below
Mixed Quest Blues
When you use mixed quest dungeons with the randomized dungeon rooms flag, things can start to get a bit interesting in what rooms can show up where. Some of this is theory, as they are extreme outlier cases, but after a discussion with Fred, have been deemed possible
Second quest stairs CAN end up in first quest dungeons
Upon looking at drop locals for some of these second quest stairs, it seems possible that you may end up with a second quest stair room in a first quest or shapes dungeon that contains an item. For this to happen, drop locations would need to line up for the two rooms that are being swapped.
An example is the 2x5 stair room in 2Q8 that contains a key - that key has the same drop location as the key in the scatter block room before Aquamentus in 1Q1 - so, in theory, it's possible to have a stair room with a drop on the floor in a 1Q dungeon (and shapes, since shapes uses 1Q dungeon drop locations)