Given the following context:

The building was sold in 1549 by Buonaccorso Pitti, a descendant of Luca Pitti, to Eleonora di Toledo.  Raised at the luxurious court of Naples, Eleonora was the wife of Cosimo I de' Medici of Tuscany, later the Grand Duke.  On moving into the palace, Cosimo had Vasari enlarge the structure to fit his tastes; the palace was more than doubled by the addition of a new block along the rear.  Vasari also built the Vasari Corridor, an above-ground walkway from Cosimo's old palace and the seat of government, the Palazzo Vecchio, through the Uffizi, above the Ponte Vecchio to the Palazzo Pitti. This enabled the Grand Duke and his family to move easily and safely from their official residence to the Palazzo Pitti. Initially the Palazzo Pitti was used mostly for lodging official guests and for occasional functions of the court, while the Medicis' principal residence remained the Palazzo Vecchio. It was not until the reign of Eleonora's son Francesco I and his wife Johanna of Austria that the palazzo was occupied on a permanent basis and became home to the Medicis' art collection.Land on the Boboli hill at the rear of the palazzo was acquired in order to create a large formal park and gardens, today known as the Boboli Gardens. The landscape architect employed for this was the Medici court artist Niccolò Tribolo, who died the following year; he was quickly succeeded by Bartolommeo Ammanati. The original design of the gardens centred on an amphitheatre, behind the corps de logis of the palazzo. The first play recorded as performed there was Andria by Terence in 1476. It was followed by many classically inspired plays of Florentine playwrights such as Giovan Battista Cini. Performed for the amusement of the cultivated Medici court, they featured elaborate sets designed by the court architect Baldassarre Lanci.

answer the following question:

What is the name of the structure Cosimo had Vasari enlarge to fit his tastes on moving into the palace? 

Palazzo Pitti