WHEN WE HEAR the word “suit,” most of us obediently picture a tailored, lapeled jacket with a pair of straight-legged trousers, cut from a sober wool fabric, or perhaps a khaki cotton for summer. While that uniform still rules at most offices and formal events, designers are reimagining the suit, unstiffening its fabric, deregulating its form. They’re taking the basic idea of a matching jacket and pants and mixing up its elements.

A cotton jacket may button all the way up the neck while its complementary pants slouch like...