How to install this double switch
Sorry about using this as an extension of the comment, there is no place in the comments for sketches to depict what is needed.

This is an  illustration to add to the comment I made about a wiring diagram, to help show my referral to a small sketch. It can be a simple line drawing. scanned and posted or drawn with a program on your computer, like Paint for Windows or a Mac equivalent.



It would need to be made a little more extensive to cover all floors.

It really should take an electrician with a tone box to diagnose where the wires go to and from.... But there is hope as long as the conditions are described accurately