The group includes San Antonio-based Lion Fund and Western Sizzlin Corp., a steakhouse chain based in Virginia.
According to the filing, two members of the group met Aug. 13 with Steak n Shake Chairman Alan Gilman to discuss the company's operations and plans. On Aug. 16, the group sent a letter to the company asking that two of its representatives be included as nominees for board election at the annual meeting later this year.
The group did not say whether it believes Steak n Shake should be put up for sale. In June, an investment group based in Dallas disclosed that it had amassed a more-than 9-percent stake in the company. That group said it wanted Steak n Shake to explore a sale or other options to boost returns for shareholders.
Steak n Shake shares this morning were trading at $15.48, up 68 cents on the day.