The sacred dragons ornating the S-shaped supports most probably refer to the coat-of-arms of the celebrated Boncompagni Roman dynasty. Cardinal Ugo Boncompagni was elected pope on May 13, 1572. His coat-of-arms shows a dragon with a truncated tail, which is the evil part of this imaginary animal.
The Boncompagni Ludovisi had a palace in Rome in Piazza Colonna. When the palace was pulled down to enlarge the central part of Via del Corso, the Boncompagni Ludovisi built a new very large palace on the site of their casino.
Interestingly, the dragon motif is also featured on the coats-of-arms of other Roman families, such as the Borghese and Del Drago.