Born on the East Coast, he moved to Los Angeles in his late-twenties. In addition to doing stand-up comedy, Alexander also began appearing in supporting appearances on many sitcoms (Full House) and other series (Matlock). Alexander's film credits include supporting roles with stars such as Tom Hanks, Steve Martin, and Jim Carrey Jason Siegle, in such films as Roxanne (1987) and Punchline (1988) and Forgetting Sarah Marshall.
He also appears in Comedy Central's Best of the Improv, Vol. 5 (2003) and Comedy Club Greats with Jerry Seinfeld (2007). In recent years Alexander is frequently in Las Vegas, Nevada, performing his comedy alongside Tom Jones and others. His most recent film is Five Year Engagment (2011). He has appeared on the Jerry Lewis MDA Telethon as well.
His stand-up routine focuses primarily on his large size, constantly poking fun at his weight and is known for pulling his pants up to his chest during his routines. But as Jay Leno has said, Max's material is as relevant today as any "young" comic.
One thing about Max that embarrasses him is his giving heart. He is not only known as the go-to person when you need someone to perform for a charity, but he has also helped countless artists, be it a comic, musician, dancer or actor get started in their careers, which showed when they honored him at his benefit.
As of May 2009, Max will be one of the only comics to perform on The Tonight Show Starring Johnny Carson, Jay Leno and Conan O'Brien.