America’s coffee market is getting too crowded.

Consumers’ hankering for caffeine and quality coffee has fueled a big build out of cafes in the last five years, especially in dense urban areas such as New York, San Francisco and Portland, Ore. There are now nearly 33,000 coffee shops in the U.S., including those run by big chains such as Starbucks, up 16% from five years ago, according to market research firm Mintel.

The...