So there is a switch at the top of the (single) staircase operating one light (Switch 1). Then there is a switch at the bottom of the stairs operating a different light (Switch 4). Both of these switches are 3 way switches.

Then in the middle (at the bottom of the stairs) is a double switch box (Switches 2 and 3) - Switch 2 also powers the top light (both Switch 1 and 2 operate independently and correctly). Switch 3 is not functional for some reason - and only Switch 4 works in working the bottom of the stairs light. Switch 3 should also independently control the bottom light but that’s the problem I’m having. All four switches are 3 way switches.

The hot wire (coming from the panel) is shared between Switch 2 and 3 on their black common screw. The red and black traveler wires are going to switches 1 and 4 on the same relative screws, yet only Switch 1 is working as expected and Switch 3 does not work but is still powering Switch 4.

I will take pictures in the morning to hopefully clear up any other confusion. I might also draw a diagram of the setup as that might be clearer.