The U.S. Supreme Court may have to bless the National Labor Relations Board’s plan to narrow the test for determining when businesses are “joint employers” and should share liability for labor violations, according to legal scholars.

A federal appeals court put the NLRB’s joint employer proposal on a likely course for the highest court in the land when it upheld the more expansive standard from the board’s contentious Obama-era decision in Browning-Ferris Industries. The now Republican-controlled board is developing...