For 80 years, Frank Pepe’s pizzeria has found world renown selling pizza in New Haven’s Wooster Square. Now, the famous pizzeria has opened two new restaurants outside of New Haven — and more could follow, perhaps even beyond Connecticut, according to a businessman approached by the restaurant as a potential investor.

Last year, Pepe’s joined forces with an unnamed business consultant and opened a second eatery in Fairfield, Conn., followed by a third in Manchester, Conn., two weeks ago. Those are only the first of many new locations the restaurant is tentatively planning, the businessman said. The source spoke on the condition of anonymity because the restaurant had not publicly acknowledged any such plans.

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Anthony Rosselli, one of the seven grandchildren who now own Frank Pepe Pizzeria Napoletana, said the restaurant has no firm plans to expand further but would consider such a move if the Manchester location thrives as the pizzeria in Fairfield has. The most important key to the restaurants is to replicate the Wooster Square ambiance and not lose the legendary quality of its pizza, Rosselli said.

“Anything is possible given the success to date,” he said. “[But] we don’t have any intention to develop a big chain or a big franchise or anything like that.”

According to the source, Pepe’s plan is to continue opening new pizzerias throughout Connecticut in addition to the two satellite locations in Fairfield, a city of 60,000 to the west of Bridgeport, and Manchester, a suburb about eight miles east of Hartford. The source said he was approached by associates of the pizzeria and was asked to consider investing in the new restaurants.

If the Connecticut eateries are successful, the expansion would continue into the rest of New England and perhaps beyond to other parts of the country, according to the source. Likely to be targeted first are college towns, like Amherst, Mass. — home of Amherst College and the University of Massachusetts Amherst — and Kingston, R.I., where the 19,000-student University of Rhode Island is located, he said.

Rosselli said he was not familiar with those plans, but he said he could not rule out further expansion.

For the Fairfield location, the restaurant replicated its famous brick oven “to the square inch,” he said. They fussed with recipes to ensure everything was an exact duplicate of the New Haven location and that the ingredients were the same, which he said they were. He said they were worried about whether the water in Fairfield would be different from that in New Haven, and how that might affect their pizza — but a test proved the water no different.

Still, opening the Fairfield location was a thoroughly frightening experience for all involved, Rosselli said. He said he recalled his feeling pulling the first pizza out of the new oven: Would it be the same?

He said it was. And the restaurant has been “extremely successful,” he said.

Hoping to expand beyond one or two locations is common for many restaurateurs, said Simon A. Flynn, the president and chief executive officer of the Middletown, Conn.-based Connecticut Restaurant Association. Because restaurant profit margins are typically very thin, adding other locations can increase an eatery’s buying power, as well as provide opportunities for long-time restaurant employees to move into additional managerial positions that would not otherwise be available, he said.

Pepe’s is in a good position to expand, if for no other reason than that it is already widely respected as a pizzeria in Connecticut and beyond, he said.

“The essential ingredient, if you will, is the success itself of the restaurant or the few restaurants that you’ve run,” Flynn said. “In my estimation, Pepe’s has been around so long, they know what they’re doing, they know what their product is, they won’t vary from the quality and the constancy of their product.”

Jeremy White, the editor in chief of Pizza Today magazine, said he thinks a large expansion could create for Pepe’s a problem that Uno Chicago Grill experienced after growing from a single Pizzeria Uno in Chicago into a national chain — a loss of recognizability and distinctive flavor.

“If you’re going to become a chain, you’re going to have to standardize everything — your procedures, your service, your uniforms, your food,” he said. “That’s going to be very difficult for Pepe’s to do on a national level, considering the pizza they make. It’s so high quality, it’s so unique.”

But Rosselli said there is no reason to worry. He said the restaurant would stop expanding if the owners sensed the quality of its pizza was not being matched at each new pizzeria.

If that were the case, he said, “I couldn’t go to sleep at night.”