SAN FRANCISCO—Dozens of major law firms are lining up against their corporate clients in an awkward faceoff at the California Supreme Court that lays bare the increasing tension between companies’ expectations of loyalty and Big Law’s economic incentives to take on more and more business.

In papers filed last week, more than 50 law firms including Arnold & Porter, Latham & Watkins, Sidley Austin and Wilson Sonsini Goodrich & Rosati urged the state high court to adopt a ruling that would allow them to represent clients with opposing interests, though not in the same matter, through the use of broad conflict waivers—and ensure they still get paid.