Maximum number of disjoint clue-sets that determine the same Sudoku solution?

"Do sudoku answers always have a single minimal clue set?" No. Solved Sudoku puzzles may have more than one set of disjoint clue-sets. And those clue-sets can vary in difficulty, so one might be easy and another diabolical, even though their 81-number answers are identical.

Gareth McCaughan poses an interesting question:

I wonder what the maximum number of disjoint clue-sets that determine the same solution is. Obviously no bigger than floor(81/17)=4, given that 17 is the minimum number of clues to make a unique solution; I bet 3 is easy but 4 might be difficult or impossible. (On the handwavy grounds that 81 is nearly 5*17, my guess is that 4 is possible.)

So, is it 2, 3, or 4?