This is campo dei Gesuiti, of the Jesuits. The story of this campo began around a thousand years ago, when the Crusades were being launched in the middle-east. Many of the crusaders who came back, did so with all sorts of battle wounds and injuries, and so an association of monks was formed, called the Crociferi, whose job it was to take care of the veterans who’d made it back.
The big building to the right and those opposite the church were all property of the Crociferi, whose intentions were originally very honourable; but once the crusades were over, they had more time and more money which they began to spend in less honourable ways. And so in the late 17th century, with the help of the Pope in Rome the Jesuits essentially took hold of the property, and among various changes, restructured the lavish façade of the church to show off their own wealth. You’ll notice the twelve disciples looking up to the Holy Mary.
Aside from religious entities, this campo was home to many guilds and corporations, famously the Scuola dei Sartori, of the tailors and if you look for house number 4881 you’ll see two low-reliefs depicting a pair of scissors to mark their workplace.