The SQ, with the speed grip mounted, does two cranks of the 35mm SLR-like winder
- wind 1 = lower mirror, cock shutter
- wind 2 = advance film to next frame
Usually, after wind 2, and the film is on the next frame, the interlock pin in the back protrudes into the body, activating the interlock whick permits the shutter button to fire.
When the multi-exposure level is actuated, the same sequence occurs but no film is advanced.
From your description, I can only guess that perhaps you loaded the film in a manner which does not actuate the film-advanced mechanism so the counter goes to the next number and the interlock pin does not protrude into the body. If you remove the dark slide with the back off the body, you should see EMULSION...if you loaded the film magazine wrong, you will see the backing paper.