The Steak n Shake Co. has offered to acquire all of the outstanding shares of Fremont Michigan Insuracorp Inc. in a deal that could be worth almost $37 million.

Indianapolis-based Steak n Shake is offering $24.50 per share, an 11.3 percent premium to Monday's closing price, for the more than 1.5 million shares it doesn't already own in the tiny Michigan insurer, which provides insurance to individuals, farms and small businesses.

Steak n Shake disclosed that it had purchased a roughly 10-percent stake in Fremont in October, shortly after CEO Sardar Biglari said he intended to transform Steak n Shake into a holding company to pursue purchases “either related or unrelated to its ongoing business activities.”

The company has not revealed its plans for Fremont, but observers say Biglari wants to use the firm's $60 million investment portfolio to fund more acquisitions, following in the footsteps of his investing hero, Warren Buffett.

Buffett's Berkshire Hathaway acquired its first insurer in the 1960s and now funds billions of dollars in investments through the portfolios of its insurance companies.

Biglari, a 32-year-old hedge fund manager, last week initiated a 1-for-20 reverse stock split that has elevated Steak n Shake shares above $290 apiece, the highest among listed restaurant companies. The move was another nod to Buffett; Berkshire A shares trade for about $99,000.

The Fremont deal would be the second major acquisition for Steak n Shake this year. In August, the company announced it was buying Virginia-based Western Sizzlin Corp.—another firm where Biglari is chairman and CEO—for $39 million.

The moves come on the heels of a fledgling turnaround for Steak n Shake, which this year snapped a 14-quarter streak of declining same-store sales.