Breakfast burritos, anyone? 5 things Bill Ackman could lobby Chipotle to change

Chipotle restaurant workers in Miami
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Breakfast at Chipotle Mexican Grill?

That's one change activist investor and minority stake owner Pershing Square may press for at the burrito chain, Credit Suisse analysts in a note to clients.

On Tuesday, the Bill Ackman's hedge fund revealed in a filing that it has amassed a 9.9 percent stake in the fast-casual restaurant company, whose sales have been severely dented in the wake of several foodborne illness outbreaks at its locations last year.

Pershing Square declined to comment on possible tweaks it would want Chipotle to make. But Credit Suisse laid out these five potential changes Pershing may push for management to enact.

Drive same-store sales through new initiatives

Sales at established Chipotle restaurants have nosedived since news of foodborne illness at locations in 15 states came to light in the past year. Same-store sales dropped 26.5 percent during the first six months of this year even as the chain ramped up its promotions and improved its food-safety procedures.

Credit Suisse thinks these new efforts could include adding breakfast to the menu, improving digital engagement, new beverages or possibly even adding a drive-thru option.

A board seat for Pershing

Pershing Square has already signaled it intends to speak with Chipotle's management and board about "governance and board composition, business, operations, cost structure, management, assets, capitalization, financial condition" and strategic plans.

Credit Suisse expects Pershing to seek a seat on the board to bring its ideas to the table and possibly advocate changes to senior management.

Shift marketing

Since seeing sales plummet, Chipotle has increased its promotions to get customers back. Various promotions have included "BOGO" offers, its first-ever customer rewards program called Chiptopia and promotions targeting college students and families.

Credit Suisse said it expects Pershing to urge the chain to shift its marketing away from these discounts and toward building back its brand.

Seek more aggressive international growth

Currently, Chipotle operates more than 2,000 locations but just 24 are outside the United States. Credit Suisse analysts expect Ackman's firm to push Chipotle to look more closely at potential international growth.

Focus on existing restaurants

Chipotle has been expanding at a steady clip, while also exploring new concepts, such as Pizzeria Locale and Tasty Made, a burger restaurant set to open this fall in Lancaster, Ohio.

Credit Suisse said it expects Pershing could urge Chipotle to slow this domestic growth and cut back on its new concept investment in order to focus on current restaurants at its flagship chain.

Already Chipotle has indicated it's going to be more judicious in its expansion. In late July, co-CEO Monty Moran said the company is taking a more conservative approach as it assesses future openings.