I need a healer!
We've started playing a variant of Zendo that we call dual Zendo.
Instead of making one rule the master instead makes two (which should be a bit simpler than whatever your current level is) and builds the usual 2 starting koans. The first koan should conform to both rules and is marked white. The second should fail both rules and be marked black. The game now proceed as normal except that each koan the students build are checked for both rules and marked white or black if it conforms/fails both rules. However if it fails one of the rule and fits the other it is instead marked green.
During a mondo a student may guess that a koan will be marked green by putting both his white and his black guessing stone into his hand.
When making a guess students must make a guess as to what the 2 rules are and in case of a wrong guess the master must build a counterexample as usual (the counterexample may be a "green" koan).
My last rule was:
A koan must consist of exactly 2 colors
A koan must have less small pieces than other (medium & large) pieces
This is a neat idea which makes the most sense (I think) for a group that's played a lot of binary, one-rule zendo.
Logically speaking, of course, two rules is equivalent to one ambiguous rule assessed using a supervaluationist semantics: that is, it unambiguously applies only if it applies on all readings, it is unambiguously false only if it fails to apply on all readings, and it is indeterminate otherwise. Once you have that formal structure, three-rule and n-rule generalizations are obvious. Of course, n-rule Zendo would be an unplayable mess for some n.