My understanding of pages 152-153 of your manual is that you have to capture the correct number of frames (2 or 3 as chosen in the menu) in order for the "multiple exposure" sequence to be complete.

As @alen mentions in his comment above, burst modes will mean those 2-3 frames are captured relatively quickly, but in other shooting modes, you still have to go through all the steps of acquiring a complete frame for each frame that makes up the multiple exposure.

For single shot, that simply means taking two pictures. The same applies in mirror lock-up mode BUT MLU requires two button presses to acquire one frame (see pg 83 of your manual for MLU details), so the process must be repeated for each subsequent frame required to complete the Multiple Exposure sequence. And it is a sequence, it is initiated and can be cancelled via the shooting menu. See pg 154 for "Interrupting Multiple Exposures".