Just what Sonia said, all of the variants sound right aside from the variants with "can". Also note that "may not" means that something is prohibited, while "might not" means that something isn't likely to happen. This makes "He may not like the design" an unlikely situation, as if someone prohibited the person to like the design. These are also called modal verbs (rather than model words).

They are all correct, but using 'can' here is a little unusual, because you then say if liking something is in this persons power, as if he would be a robot. It is grammatically correct, but if you use these sentences in speech you can use may instead of can to make ik more natural.