The Steak n Shake Co. is taking a dramatic turn away from its core business with a bid to purchase a Michigan insurer in a deal valued at almost $37 million.

The Indianapolis-based burger chain, now operated as a holding company with activist-investor-turned-CEO Sardar Biglari at the helm, has offered to acquire the outstanding shares of Fremont Michigan Insuracorp Inc. for $24.50 per share in cash and stock, an 11.3 percent premium to Monday's closing price.

It's the second major deal this year for Steak n Shake. The company acquired Virginia-based Western Sizzlin Corp.—another restaurant chain where Biglari is chairman and CEO—for $39 million in a deal finalized this fall.

While Wall Street applauded the latest deal, sending shares up more than 17 percent to $345 in morning trading, local investment advisers say the company is wandering away from its specialty into uncharted territory.

"It's hard to see how burgers and insurance policies go together,"  said George Farra, co-founder and principal of Woodley Farra Manion Portfolio Management. "I'm very concerned that one of the few local publicly traded companies—its focus is being diverted to build a financial services empire without much of a track record behind it."

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 $300 apiece, the highest among listed restaurant companies. The move was another nod to Buffett; Berkshire A shares trade for about $99,000.

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