Is there a number M such that the following is true:

If a pseudo-puzzle with 16 clues has M different completions, then we cannot add a clue to make a valid puzzle (1 completion) with 17 clues.

What is the smallest such M?

Another way of looking at it: suppose you have a valid sudoku with 17 clues. You remove one clue. Is there any limit on the number of completions the resulting pseudo-puzzle can have?