The project design, by the Bjarke Ingels Group, would dramatically “float” a collection of staggered apartment and office blocks on stilts over the old Allapattah Produce Center. The center’s three industrial-style warehouses, each the length of two football fields and still operating as a produce market, would be converted into retail, a trade school and possibly even an urban farm.

The eight-acre center would also be planted with lush landscaping and rooftop gardens, turning what’s now a stretch of treeless asphalt and concrete into an island of green...