The company behind Burger King wants to take over fast food — and that could mean buying Papa John's (QSR)

Restaurant Brands International, the company behind Burger King and Tim Horton's, recently snapped up popular fast food chain including Popeye's.
Credit Suisse says investors want more, and predicts Papa John's, Wingstop, or Yum Brands could be next.

After earlier this year, investors in Restaurant Brands International, the company behind Burger King and Tim Horton’s, are hungry for more.

Credit Suisse has been talking to investors ahead of the company’s earnings next week, and finds they’re much more interested in expansion than a special dividend.

"We found that the majority of investors would prefer to see QSR add more brands to the portfolio rather than a one-time special dividend, even if the deal was not highly accretive at the outset or if it takes time to find the next acquisition," analyst Jason West said in a note Wednesday.

The bank modeled potential buyouts in a note last week, based on the roughly 33% premium Burger King paid for Tim Horton’s in 2014. Here are the top choices:

The Kentucky-based pizza chain is top of Credit Suisse’s list for an RBI buyout, but the bank still says "we do not view a deal with PZZA as imminent or necessarily a high probability." Nevertheless, pizza isn’t on any current QSR-owned menu, and a 30% stock premium would be barely above PZZA’s all-time high.

"There is a strong case to be made for benefits of global scale," Credit Suisse said of the company behind Pizza Hut and KFC.

"However, many of these benefits are difficult to model and may be more than offset by: 1) dilution to existing shareholders (our base case is 80% of funding via new equity), 2) menu overlap between KFC and Popeye's and 3) potentially too much complexity in managing six of the world's largest fast food brands under one roof."

QSR already owns a robust chicken menu in its Popeye’s chain, but a merger with Wingstop could still result in $20 million in cut costs, according to the bank’s analysis.

Other possible — though unlikely — mergers include Chipotle, which has struggled to revive its slumping stock price after a string of food poisoning outbreaks, Buffalo Wild Wings, Dunkin’ Brands, Subway, and Little Caesars, Credit Suisse says.

Business Insider has reached out to QSR, as well as the three potential acquisitions about the proposed mergers and will update this post if comment is received.

Fast food has been a hot space for M&A activity lately, especially for private equity. Europe's JAB Holdings has amassed an empire of fast-casual coffee and sandwich restaurants including Panera Bread, Krispy Kreme, and Peets Coffee.

Credit Suisse maintains its outperform rating for QSR stock, with a price target of $74 — 9.4% above the stock’s $67 price Wednesday morning. Shares of QSR are up 44% so far this year.