The Raphael and Michaelangelo room is meant to capture a rare moment in Florentine history when the Medici family, the dynasty that ruled from 1434 to 1737 with a few interruptions, did not dominate the city’s politics and culture. Between 1498 and 1512, the family was in exile and Florence became a republic under Piero Soderini. Artists who once flocked to the Medici turned to other patrons “who competed to procure the most masterpieces,” Mr. Schmidt said. “It’s a reconstruction of the patrons who tried to outdo each other.” Apart from the popes Julius II and Leo X, only the Doni family managed to commission works from both Raphael and Michelangelo.

Mr. Schmidt has positioned a Hellenistic-era head known as the Dying Alexander next to the Doni Tondo, in part to accentuate Michelangelo’s relationship to antique sculpture. The Uffizi has one of the world’s greatest collections of antique sculpture, though it is often dwarfed by the richness of the painting collection.

Raphael’s “Madonna of the Goldfinch,” also in this room, was painted for the Nasi family, another prominent dynasty of the time. It has been moved here from a long corridor in the gallery so packed with paintings that many visitors paid it no attention.