The new lawsuit, filed by an investor from Pennsylvania in U.S. District Court in New York, seeks to block Apple from moving forward with a February 27 shareholder vote on two proxy proposals.
One of the proposals is the same measure Einhorn targeted that would eliminate from the company charter Apple's ability to issue preferred stock.
The other, which was not part of Einhorn's case, involves an advisory "say-on-pay" vote for shareholders to weigh in on Apple's executive compensation. The lawsuit accuses the iPhone maker of failing to disclose details of how it determined top executives' pay.
The plaintiff is Brian Gralnick of Elkins Park, Pennsylvania. He has been an Apple shareholder since 2007, the lawsuit said. It does not list the size of his stake.
"The case has some overlap with the Einhorn case, but it is a broader case," said Arnold Gershon, a lawyer for Gralnick at the law firm Barrack, Rodos & Bacine.
An Apple spokesman had no immediate comment.
Gershon also said his client would seek to be heard at a February 19 hearing in Einhorn's lawsuit.
Einhorn and his Greenlight Capital sued Apple on Thursday in the same court as part of a bigger effort to get the company to share more of its $137 billion pile of cash and marketable securities with investors.
He accuses Apple of violating a Securities and Exchange Commission rule prohibiting companies from "bundling" unrelated matters into one proposal for a shareholder vote.
Apple was due to file court papers replying to Einhorn's case by the end of the day. On Tuesday, Apple Chief Executive Tim Cook said the board was considering Einhorn's proposal for the company to issue preferred stock and return more cash to investors, but he called the court challenge "a silly sideshow."
The claim of inadequate executive pay disclosure in Wednesday's case follows other lawsuits in recent months filed against companies seeking injunctions ahead of say-on-pay votes. The cases have been met with varied success.
In the Apple case, the plaintiff says shareholders do not have adequate information to make a decision on executive pay at the company and he is seeking an injunction against the vote.
The case is Gralnick v. Apple Inc, U.S. District Court, Southern District of New York, 13-0976.
© Thomson Reuters 2013