IMAGINE A FOOTBALL-FIELD-SIZE ice-cream parlor. Now, imagine that every flavor is vanilla. That might be the best way to describe what the market for plain white T-shirts looks like right now. “We sell white tees from everyone,” said Kevin Harter, vice president for men’s fashion direction at Bloomingdale’s. Indeed, the store’s selection ranges from Calvin Klein Underwear three-packs ($39.50) to designer styles from brands like Rag & Bone for upward of $100 per tee.

Do men really need so many versions of something so...