Until the new Una Pizza Napoletana came along, I didn’t think it was possible for a restaurant to fight itself to a draw.

In name at least, this is the fourth incarnation of the pizzeria that Anthony Mangieri founded in 1996 in Point Pleasant Beach, N.J. He has never run more than one Una Pizza Napoletana at a time; each time he moves to a new location, he closes the old one. In the East Village (2004-9) and San Francisco (2010-17), he essentially stuck to the routine he had established in New Jersey.

At the two-month-old location on the Lower East Side, though, he is in business with two chefs, Jeremiah Stone and Fabián von Hauske Valtierra, whose sensibilities are wildly different from his own. Their two other restaurants, Wildair and Contra, are very contemporary and European in outlook. A meal at either one makes it obvious that Mr. Stone and Mr. von Hauske have carefully studied Copenhagen’s foremost exponents of fermentation and foraging. Nothing about Mr. Mangieri’s rigorously traditional pizza indicates that he could find Copenhagen on a map.

The three of them do have common traits. They take their cooking extremely seriously, favor simplicity and aren’t interested in easy ways out. So their collaboration — Mr. Mangieri is the pizza guy, of course, while his new partners handle appetizers, desserts and drinks — might not be doomed, but it isn’t exactly off to a promising start. The problem isn’t the common one of strengths in one area undermined by bad performance in others. Una Pizza Napoletana is almost all strengths, but they’re at war with one another.