Boston guitarist Tom Scholz has 34 patents to his name, including the Rockman, a now discontinued headphone amp that was favored by many touring musicians.
Greg Graffin, the lead singer with Bad Religion, has a PhD in (I think) zoology from Cornell and has an extinct bird named after him, Qiliania graffini.
Robert Leonard, original Sha Na Na lead vocalist, has a PHD (I think) in linguistics from Columbia. He is now a professor and the director of Hofstra University’s Institute for Forensic Linguistics, Threat Assessment and Strategic Analysis.
Sterling Morrison, of the Velvet Underground, earned a PhD in mediaeval literature from the University of Texas in Austin.
Tom Morello of RATM graduated from Harvard.