More than three dozen universities are spending millions of dollars on Wash­ington lobbyists to help shape patent ­litigation reform as the U.S. Senate crafts a plan to stop abusive practices.

The universities last year spent at least $11.4 million lobbying on legislation intended to reduce the litigation clout of so-called patent trolls, among other issues, according to congressional records. Cornell University, Pennsylvania State University, the University of Illinois at Urbana-Champaign and the University of Pittsburgh are among some of the leading research institutions that have deployed lobbyists to those ends.