Tom,
Of course it can be extended beyond two monks.
As shown above, if two (and only two) monks have the red spot then they will commit Hara Kiri on day 3.
If, on day 3 you check all the other monks and only see 2 spots then you expect them to top themselves. If they do not do so, then as you know of only two red spots, and each of them clearly knows of only two, then each of you can logically decide that you must have the third and must commit suicide.
For any number of red spots the realisation will only dawn on those with a red spot the day after the number of red spots they can count has not resulted in a mass suicide.