Another thing to check is that there is a small button on an FM to allow double exposure. It is on the top of the camera to the right of the eyepiece next to the the shutter speed dial. It should be towards the wind handle, if it is toward the eyepiece when you wind it only resets the shutter. check to be sure it is springing back to the right freely, and that you are not bumping it while winding. I doubt you are bumping it while winding as it is hard to use normally, but it may not be springing like it should. I hope you get it sorted out, the FM is a really fun camera that can take far better shots than I am able to.
Just a guess as to what could be wrong on my part.