Uber Technologies Inc. could face unintended consequences of successfully keeping a class action out of court: 12,500 individual cases in arbitration that could put the company on the hook for nearly $19 million in fees.

At least that’s the hope of plaintiffs attorneys who just hit the ride-hailing giant en masse, asking a San Francisco federal judge to compel Uber to answer to thousands of arbitration claims filed in recent months—and to pay all the associated costs, as required by employment agreements.