SAN FRANCISCO — Wielding the U.S. Supreme Court’s new case on fee shifting, some 55 finance and technology companies are taking aim at one of the nation’s largest nonpracticing entities, accusing it of causing expensive and unnecessary multidistrict litigation.

A squadron of corporate defendants led by Twitter Inc. and Yahoo Inc. are moving for fees against companies owned by Acacia Research Corp. and cloud services provider j2 Global Communications, saying the two concocted “a calculated, deceitful plan” to divvy up a family of patents and then assert conflicting interpretations of them in different cases.