As they converted and baptized they needed a "new" surname to go by-- And in these cases, the surname of the current Pope of the times applied to them: that's why the palace is called "Boncompagni-Corcos". If anything, the Corcos became even more influent and powerful, and profitted "to fix" their residence, among other things.
The structure is quite simple and elegant, in an attempt to take inspiration from Palazzo Farnese, with its light yet powerful Reinassant vibe.
Travertine and bricks are another hint in this sense-- You can feel the baroqueness of the architecture only in the decorations of the windows and the mascheroni decorating them.
Once inside, we're welcomed by a tiny yet nice courtyard, featuring an interesting interpretation of Ionic capitals:
The achitecture bits were fixed by Giovan Antonio De' Rossi, and the painting decorations are the job of Carlo Cesi-- The decorations followed the trend of the mythological themes imbued with edifying morals, allegories, or scenes of the Old Testament.
In this sense, the most important artwork is the one dedicated to the marriage between Maddalena Boncompagni and Filippo Camerata of Ancona, dated 1661, September 22th, proudly celebrated by Pietro with a fresco depicting the marriage between Ariadne and Bacchus...
One of the most interesting rooms, in my opinion, was the tiny yet richly decorated little private chapel.
Besides the beautiful marble decorations and the fine paintings, it hosts a venerated icon of Virgin Mary, said to be miraculous during the Pestilence of 1657, and an extremely cute example of a tiny, home nativity scene to decorate during Christmas time--!