When you frame for an opening, whatever size the door happens to be....you need to add 2 1/2 inches for the rough opening to have the least amount of problems.
Example...your 32 inch door is the actual size of the door slab itself.
Now yow need to add the jambs which are 3/4" each side.
Next you need a 1/8 inch gap on each side of the door slab, between the door and jambs to open and close the door.
Next you need a 3/8 " between each door jamb and the jack stud ( not cripple,or headers those are at the top of the door),left and right sides, to shim the door so it is plumb in the opening and has room for movement once the new construction starts to move.
so 3/4 jamb+ 3/4jamb= 1 1/2
1 1/2 of jambs + 1/8 gap+ 1/8gap= 1 3/4
1 3/4 + 3/8gap at studs + 3/8 gap at studs = 2 1/2" total added to a 32" door equals a 34 1/2 inch rough opening.
So no you "Will" not make it with just removing a stud.
You need to lay out all your doors and windows on center then do you 16 on center.
Try a framing book at your local library...they are free.