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With the choice of four of the world’s greatest architects, how could David Levinson ever settle on just one to build a new tower at 425 Park Avenue?

“That’s my next job, to find three more sites so I can build all these buildings,” Mr. Levinson joked, seated at a conference table inside his sleek white offices on 57th Street on Monday. He was surrounded by renderings and models by Zaha Hadid, Richard Rogers, Rem Koolhaas and the winning architect Norman Foster.

“For us, it was really a blend of what’s the right concept for Park Avenue, a place that has not had a new building for almost 50 years, an avenue that is quite possibly the most important commercial boulevard in New York City, quite possibly the United State, and what is the place of a new build down the street from Seagrams and Lever House, two of the greatest buildings ever built,” Mr. Levinson explained. “We had to determine for that setting what’s the right firm. So really, it’s a blend of the concept and the firm we can work with.”

Mr. Levinson emphasized that this was not a traditional architecture competition, where he was selecting a design so much as a firm. He acknowledged that Lord Norman Foster had a head start, but as the competition got underway, that choice became harder to make.

“Things we knew early on about the Foster organization, it’s a very deep bench with a great deal of knowledge about office buildings,” Mr. Levinson said. “There is an emphasis on function, the techtonic aspect, but also an emphasis on form, how it fits into the Park Avenue context and makes an impact.”

Foster proposed a set of three floating towers—Mr. Levinson called them separate buildings connected by a central spine—with each higher segment held aloft by dramatic trusses. In the spaces between the office blocks are vast open spaces, some 42-feet high, that will be open to building occupants and occasionally the public.

“We wanted to address the public realm, how does a building fit in to the public realm, the way people approach the building,” Mr. Levinson said.

This was true of all the designs, but the way they addressed them were different. Rem Koolhaas conceived of a dramatically torqued building, with retractable walls throughhtout to reveal the spaces or protect them from the elements. Richard Rogers created what Mr. Levinson joked was an “Adirondack park.” Like Mr. Foster’s plan, there are three discreet office volumes, but here they are held up by a robust orange structure with diagonal cuts to make room for pocket parks, planted with tall pine trees—certainly nothing else like it in New York. Zaha Hadid created a sinuous building that resembles a giant white flower. It has cutouts at the base of the petals, in the towers four corners, which would have been open to the sky.

“Rogers we knew would have an exoskeleton, something very muscular, Zaha would create something real organic, Rem would have some movement and a very cerebral project and Foster would have elegance with an emphasis on the presence of the building,” Mr. Levinson said.

It is a challenging commission since all the firms were given the task of peeling back 75 percent of the current boxy building that sits at 425 Park Avenue, then building back up from the base that remained. This was part of a zoning quirk that were Mr. Levinson to demolition the entire building, he would actually be forced to build something smaller than the current building, about 500,000 square feet compared to 650,000.

Mr. Levinson is eagerly awaiting the Midtown East rezoning, which might remove certain impediments to his project, like a better base to the building, but he also admitted that he does not expect to build an even bigger building, even though the new zoning would allow it, up to 24 FAR, compared to the 18 FAR the building currently has (current zoning only allow 15 FAR, but since the building was built before the zoning was revised in 1961, it is bigger than that).

“We are building a bespoke office building,” Mr. Levinson explained. “I don’t think we need to go much bigger than what we have now. Around Grand Central, bigger might work, but this is the Plaza District, this is a bespoke office building, and I believe this is the right size for us.”

Mr. Levinson said he was not joking about finding a place for all these architects in his stable. “We actually do hope to work with all the firms in the future,” Mr. Levinson said. No doubt the city’s architecture cognoscenti hopes he does.