D'Amico did not reprise the role of Michael "Mouse" Tolliver in the 1998 sequel, More Tales of the City, and the role was recast with Paul Hopkins (who also appeared in the third installment, Further Tales of the City in 2001). According to the series' author, Armistead Maupin:
When asked about fears of typecasting after appearing in the stageplay Angels in America and in the Tales of the City TV series, D'Amico stated in 2003, "I did get typecast in gay roles but it now no longer worries me."
D'Amico has stated a preference for stage acting, and among his various stage performances are a production of Shakespeare’s Julius Caesar at London's Young Vic Theatre, and The Boys Next Door at London's Comedy Theatre. One of his award attributes includes a nomination for the 1992 Laurence Olivier Award for Best Actor for his role in the stageplay Angels in America. In 2003 he appeared in The Lisbon Traviata at the King's Head Theatre in London. The following year he joined the cast of Mamma Mia! in London.
