After serving up Burger King to the public, is Bill Ackman's cooking up another success story at Chipotle Mexican Grill (CMG) ?

Ackman could be looking to duplicate his successful stake in Burger King, which saw shares double in just two years after the Home of the Whopper was taken public again in 2012.

His hedge fund, Pershing Square, disclosed an option to buy nearly 9.9% of Chipotle's market cap late Tuesday, and shares climbed more than 6% Wednesday on the news. While Ackman says he plans to meet with Chipotle executives, his activist plans are, so far, unclear.

Meanwhile, Chipotle investors can learn from Ackman's longstanding thesis on fast food, or what Pershing Square and others in the industry call quick-service restaurants, or QSRs. And one of the most consistent themes in this group is franchise expansion -- an area in which Chipotle has plenty of room to grow.

It isn't hard to imagine that Ackman's maneuvers will echo how his stake in Burger King saw the market cap more than double in two years, as well as his plans for smaller, Canada-based peer Tim Hortons', which Burger King acquired in 2014 for about $12 billion. (Pershing today maintains a roughly 17% stake in Restaurant Brands (QSR) , which Burger King's holding company was renamed as after the Tim Hortons' tie-up.)

In Pershing's first-quarter letter to shareholders, he emphasized the ability to build organic growth through adding new restaurants and cutting overhead costs, a combination which he said helped boost Restaurant Brands EBITDA by 23% in the first quarter. (EBITDA is a standard valuation metric that stands for earnings before interest, taxes, depreciation and amortization.)

And while Chipotle has taken some initial steps in crossing the Atlantic, with some locations in Europe in places such as Paris, London and Munich, it is hardly a global operation. But Ackman's track record suggests that may not be for long.

At the end of last year, only 47.5% of Burger King restaurants were in the U.S., and 52.5% were abroad, and according to the company's annual filing with the SEC, Burger King has boosted its annual net restaurant growth more than fourfold since 2010, with 631 new units in 2015 vs. the 173 additions in 2010, "making it one of the fastest growing QSRs in the world."

Ackman's Burger King story began by snapping up more than 10% of Burger King's market cap after helping to arrange its 2012 IPO, which he noted in an April 2012 SEC filing that Burger King's "simple, predictable, free cash flow growth franchise" was a primary motive for taking the franchise public with the help of a specialty acquisition fund, Justice Holdings, which Ackman co-founded. Burger King had been taken off public markets in a private buyout by 3G Capital in 2010.

And in helping take the Burger King public again in 2012, Ackman also cited the benefits that Burger King was in a "process of transformation," which is certainly true of a struggling Chipotle: Shares have fallen more than 40% over the past 12 months after being panned by analysts through a slew of downgrades, largely prompted after Chipotle had to shutter scores of restaurants in Washington and Oregon after a series of E. coli cases surfaced last November.

And sales certainly reflect the negative commentary, with Chipotle sales in the six months ending in June clocking in at just $1.83 billion vs. the $2.29 billion recorded a year earlier, based on the company's most recent quarterly filing with the SEC.

Ackman's advantages this time around may be that Chipotle has a far leaner business model to rework. By sheer size and scope it looks like the Mexican food chain could fit on Burger King's Junior menu. On one hand, Chipotle listed only about 2,000 restaurant outlets in 2015, of which California's 351 more than double any runner-up state. Burger King, a global franchise, has 15,000 stores worldwide over the same period, and its sales of $17.3 billion last year trump Chipotle's $4.5 billion over the period.

And as he prepares to speak with management about his future plans for Chipotle, its worth bearing in mind his views 2015 thoughts on Tim Hortons' following its tie-up with Burger King, citing "substantial unit growth opportunistic outside of Canada," and his imperative for franchise expansion.

Real Money chartist Bruce Kamich wrote Wednesday that Chipotle's stock has recently climbed above its short-term 50-day moving average line, which generally does not indicate a time to buy from a technical perspective. "Ackman may be right or he may be wrong. The marketplace will tell us soon enough," Kamich noted. "I want to see a higher high or a weekly close above $450 to tell me that the bull is getting the upper hand."