Rika Mead got divorced a few years back, but didn’t want to give up the dream home she’d bought outside Denver. So she forged a solution she hadn’t considered in decades: She got a roommate.

Ms. Mead, 71 years old, has honed her criteria for cohabitants since then. A housemate may not own dogs, but must love Ms. Mead’s two dogs, Bindi and Baku. They must not try to convert her to their religion. (It’s happened.) And while Ms. Mead is no prude, she’s at a point in life where men aren’t welcome overnight. “I want my housemate...