According to some sources[Notes 1] the construction of the original church was financed by a certain Pietro or, according to Doge Andrea Dandolo, by Cleto Gussoni in 1148 and was surrounded by grounds, bodies of water and wetlands.

Another Gussoni, by the name of Buonavere, relative and heir of Cleto, ultimately provided vineyards and some of his other estates in the districts of Chioggia and Pellestrina.

In the monastery of I Gesuiti a member of the same family, Marco Gussoni, took his vows, miraculously cured by the then Blessed, later Saint Luigi Gonzaga.

A portrait of him entitled Marco Gussoni blessing the plague victims at the Lazzaretto of Ferrara[Notes 2] is exhibited in Ca' Rezzonico.

He returned to Venice in 1535 with a group of friends, who already called themselves the Society of Jesus (members of which are referred to as Jesuits - Gesuiti in Italian), and here they were ordained as priests.

The Jesuits in Venice determined that Domenico Rossi, who designed the Church of San Stae, was the ideal architect to do the work they needed.

[2] Lining the Tympanum are statues by Giuseppe Torretti, forming his work L'Assunzione della Vergine Maria (The Assumption of the Virgin Mary).

Between the second and third chapels stands the remarkable pulpit created by Francesco Bonazza and along the entire corridor there are "corretti", grates that visitors to the convent could look through.

The nave of the church pales in comparison to the altar, which is dedicated to the Holy Trinity, due to the presence of four pillars which support the cross vault.

Around the altar, designed by the Jesuit father Giuseppe Pozzo, ten columns support a green and white dome.

At the four corners adorning the pilasters the marble statues of the Archanges Michel, Gabriel, Raphael and Sariel by Giuseppe Torretti.