The parent company of Steak n Shake restaurants has scaled back a controversial pay package for its CEO in hopes of securing shareholder approval of the plan at a rescheduled special meeting.

Biglari Holdings Inc. canceled the previous meeting, scheduled for Aug. 24, to "correct misinformation," answer questions from shareholders and analysts, and incorporate suggestions into an incentive package for Sardar Biglari, the company's chairman and CEO.

The revised package would pay Biglari the equivalent of 25 percent of the company's annual growth in adjusted book value above a 6 percent threshold, up from 5 percent in the earlier version. The new deal also caps Biglari's annual incentive pay at $10 million, but still requires him to spend at least 30 percent of his annual incentive payment buying Biglari Holdings shares in the open market.

The new meeting is scheduled for Nov. 5 in San Antonio.

Biglari Holdings revealed details of the new incentive pay arrangement in a proxy statement filed with the Securities and Exchange Commission on Sept. 29.

The filing says the company's annual goal for book-value growth is 10 percent. Based on a book value of $300 million, if the company achieved that 10 percent target, Biglari would earn an incentive bonus of $3 million. That is in addition to an annual salary of $900,000.

Biglari Holdings also addressed criticisms of the incentive plan from shareholders and proxy advisory services that previously recommended a no vote. The companies, including Institutional Shareholder Services, warned the company could manipulate the book-value metric upward without shareholders seeing any benefit, for instance, by issuing new shares to fund an acquisition. Another concern: Measuring book value growth is not traditionally considered relevant in the restaurant business.

The company shot back that it is not a pure-play restaurant company, but rather a diversified holding company, and that "adjusted book value" would be calculated using only "items that add economic value to the company" and not financial engineering.

Any further changes to the agreement that would benefit Biglari would require shareholder approval, the document notes.

"The Company views its shareholders as true partners in the business and wants their questions and suggestions to be considered fully, clearly, and accurately," the filing says.

The company wants to redesign Biglari's pay package to reward him for a successful turnaround of the Steak n Shake chain, and acknowledge the company's transition into a diversified holding company and Biglari's responsibility for all investment decisions.

Negative reaction to the pay arrangement contributed to a swoon in Biglari Holdings shares, from a peak of $418 in early April. Biglari responded to the drop by buying up even more shares. He has spent more than $30 million buying shares this year alone.

Biglari likely would not have put forward the new agreement if he wasn't confident he'll have shareholder support to get it passed.

The shares were down about 2 percent in early trading Friday, to $322.43 each.

Motley Fool columnist Richard Gibbons called the original deal “one of the sweetest compensation arrangements I’ve ever seen at a public company”—one that would cut deeply into shareholder returns.

Ken Skarbeck, managing partner of Indianapolis-based Aldebaran Capital LLC and a columnist for IBJ, in August said the pay is too rich for such little growth. Paying Biglari 10 percent of an increase in the company’s annual book-value growth topping 10 percent would make more sense, he said.

“This guy’s trying to make 30 million bucks a year,” he said. “That’s ridiculous for some 30-year-old kid who’s running a restaurant chain.”

Biglari took over Indianapolis-based Steak n Shake Co. in a 2007 proxy fight, helped return its restaurants to profitability, then transformed it into a holding company for a diverse range of investments.

The renamed company, which relocated its headquarters from Indianapolis to San Antonio, has moved aggressively to invest or take over other firms, including a small Michigan insurer. The Steak n Shake restaurant operations remain in Indianapolis but are scaling back their office space in downtown's Century Building.