Convert 2 adjacent double gang box to 4 gang box; what are these extra wires?
You are in the conduit wiring method with metal conduit, note multicolor wires and no grounds.  Your box has a lot of thru-wires and you will need to follow them to one end or the other, pull them out, do your work and put them back in.   It helps to use them to pull in a string.  I do this all the time, and yeah, it's a PITA.  As such, I'm not sure why you are taking this on.  

Cutting them is out of the question; you simply don't have enough length to terminate them properly.  I recommend cutting  8" beyond the surface of the wall or 11" from the hole, I believe legal minimums are 3" beyond surface of wall and 6" from conduit exit, but that will be a PITA to to work with.  

Note that the right 2-gang actually is back-to-back with another 2-gang box, and it has a flush thru-nipple with that. That thru-nipple will define the positioning of the new 4-gang; that means you may need spacers to meet the wall on the left.  It will also force you to slightly move the 3 conduits in upper left; hopefully they have enough freedom of movement to allow that.  The new 4-gang must be metal (and the same thickness obviously), and must have proper conduit termination with solid grounds.  I recommend acquiring this box at a genuine electrical supply house; they will have good selection of such specialty boxes and their prices will be much better IME. 

If you are very lucky, all the wires going through that thru-nipple terminate in the box on the other wall.  That would be rather easy!  

Neutral wires must be white or gray.  I consider gray "alt-neutral" and I use them for second circuits, but there is nothing wrong with using all gray if you want to. They are not connected to the switches because neutrals normally aren't.  If you fit smart switches, join the neutral that is a partner to the hot you are switching. The prospect of fitting future smart switches, is all by itself, good justification to get some more gray wire (again, electrical supply) and replace the runs so you have the necessary slack to splice them in this box. Yes, I would do that!

It is possible that these are neutrals from two separate circuits!  If so, it is all on you to keep them separated.  It is vital not to jumble up neutrals to avoid overload. If you can put those circuits on GFCI breakers, that will keep you honest :)