It's possible with a regex. Here's one spectacularly awful way: enumerate through all the permutations of 3 out of 4 character classes. Assume the classes are A, B, C, and D just to simplify the syntax here:
(.*A.*B.*C.*)|(.*A.*B.*D.*)|((.*A.*C.*B.*)|(.*A.*C.*D.*)|(.*A.*D.*B.*)|(.*A.*D.*C.*)|(.*B.*A.*C.*)|(.*B.*A.*D.*)|((.*B.*C.*A.*)|(.*B.*C.*D.*)|(.*B.*D.*A.*)|(.*B.*D.*C.*)|(.*C.*A.*B.*)|(.*C.*A.*D.*)|((.*C.*B.*A.*)|(.*C.*B.*D.*)|(.*C.*D.*A.*)|(.*C.*D.*B.*)|(.*D.*A.*B.*)|(.*D.*A.*C.*)|((.*D.*B.*A.*)|(.*D.*B.*C.*)|(.*D.*A.*B.*)|(.*D.*A.*C.*)Well, they wanted 4 of 4, actually, and yes, I had to do custom validation. Everything except the upper-case character worked in JS, so everything "just worked" if I took that part out, but that wasn't an option.
Not to nitpick, but they wanted at least 3 of those 4. Is that possible with a regular expression or are we now into the custom validator territory?