In 1993 Grosso's monologue Mama Don't was produced by the Royal Court Young People's Theatre and put on at the Commonwealth Institute, London. It was directed by Roxanna Silbert.

A year later his first stage play, Peaches, was produced by the Royal Court Theatre in association with the Royal National Theatre Studio and put on at the Royal Court Theatre, London. It starred Ben Chaplin. According to Michael Billington, the season in which Peaches appeared (which also included Blasted by Sarah Kane) defined the historical importance of the Theatre Upstairs, a season of new writing masterminded by Stephen Daldry.

In 1996 Grosso's second stage play, Sweetheart, was produced by the Royal Court Theatre and put on at the Royal Court Theatre, London, before embarking on a regional tour. It starred Kate Beckinsale.

In 1998 Grosso's third stage play, Real Classy Affair, was produced by the Royal Court Theatre and put on at the Ambassadors Theatre, London. It starred Joseph Fiennes and Nick Moran.

His fourth stage play, Kosher Harry, was produced by the Royal Court Theatre and put on at the Royal Court Theatre, London, in 2002. It was directed by Kathy Burke and starred Martin Freeman.

Since then the Hampstead Theatre in London has produced and put on three young people's plays by Grosso.

In 2004 Grosso directed his monologue Killing Paul McCartney at the Assembly Rooms at the Edinburgh Fringe Festival. It was produced by David Johnson and performed by Jake Wood.

The same year Grosso was invited to participate in the inaugural 24 Hour Plays at the Old Vic Theatre, London, hosted by artistic director Kevin Spacey.

In 2005 Grosso wrote A Play In Swedish English And Italian for the Royal Dramatic Theatre in Stockholm, produced by Elverket.

Grosso's plays have received further productions in theatres such as the Salisbury Playhouse, and other European countries, and New York, Chicago and Los Angeles.

Grosso's work and role in contemporary theatre has been analysed in books such as "State of Play" by David Edgar (Faber and Faber, November 1999), "In-Yer-Face Theatre" by Aleks Sierz, and "The Blue Room" by Dominic Dromgoole.