Jens Faurschou grew up on the Danish island of Funen, to parents who weren’t big art-buyers but who had a ceramics collection. No, he did not come from money. “Not a dime, unfortunately,” he said.

He had a formative experience going to the Louisiana Museum of Modern Art outside Copenhagen, where three works struck him with particular force: an Edward Kienholz, an Yves Klein and an Arman.

Mr. Faurschou, 59, studied economics in Denmark, and then in the 1980s started making visits to New York, where he did his first art deal.

He learned a lesson: He liked stretching his limits. And on Sunday, the Danish dealer-turned-philanthropist is opening his third exhibition space as the newest member of New York’s private museum club. The museum, Faurschou New York, sits on a quiet street in the Greenpoint neighborhood of Brooklyn and reflects the personality of its patron: It is reticent in one sense, forceful in another.