Burger King Worldwide is no more. With the acquisition of Tim Hortons, the home of the Whopper has a new name: Restaurant Brands International (NYSE:QSR).

Technically, a burger chain and coffee shop satisfy the use of the word "brands," but the name seems to call out for more. 3G, Restaurant Brands' controlling shareholder, has a history of building conglomerates (Anheuser-Busch InBev), and it could be about to do so again. In a recent Bloomberg interview, hedge fund manager Bill Ackman -- also a top Restaurant Brands shareholder -- suggested as much, noting that Restaurant Brands may be on the hunt for additional takeover targets.

But what would Restaurant Brands buy? There are literally dozens of fast food chains the company could acquire, but a few possibilities stand out.

Potential criteria
To find out what chains Restaurant Brands may be interested in, it's worth looking at its acquisition of Tim Hortons.

3G took Burger King private in 2010, buying the then slow-growing fast food chain for a modest $3.3 billion. Under 3G's control, Burger King pursued growth and cash flow. Its strategy centered around slashing costs, selling restaurants to franchisees, and radically reinventing its menu (a process that continues today). It returned to the public markets in 2012, at a valuation of around $5 billion.

The transformation worked: Burger King's same-store sales rose in 2013 and 2014, and its earnings per share steadily increased as it added additional restaurants. By the time it announced plans to buy Tim Hortons, the stock had doubled from its IPO.

The acquisition of Tim Hortons gives Burger King's management a new brand to tinker with and expand. Virtually all of Tim Hortons locations are in Canada -- 3G can use its international expertise to take the chain global. Moreover, although Burger King serves coffee and breakfast, it is not a true competitor, allowing both chains to peacefully coexist. Finally, like Burger King post 3G ownership, Tim Hortons operated as a fully franchised business, with few corporate-owned stores.

Anything is possible, but Restaurant Brands' interest may lie with highly franchised restaurants that have growth potential and don't directly compete with its existing brands.

A move into fast casual?
Chipotle
certainly wouldn't fit the bill -- the burrito giant is growing rapidly, but has a strong obsession with corporate management, believing it can ensure a better experience for its customers if it owns and operates its own stores.

There are other opportunities in the space. Jack in the Box's (NASDAQ:JACK) Qdoba subsidy has emerged as an increasingly competent rival to Chipotle, one that has been willing to franchise (about half of Qdoba stores are franchise owned). Though management has not endorsed the idea, chatter of a potential split has emerged, and for good reason: Jack in the Box is a relatively mature, slow-growing burger chain, one that has not meaningfully increased its store count since 2010. Qdoba, in contrast, is an exciting, fast-growing concept -- its store count has risen more than 21% in the same time period. Buying Jack in the Box would give Restaurant Brands two competing burger chains, but ownership of Qdoba could be attractive.

Adding pizza to the menu
With coffee and burgers covered, Restaurant Brands could look to add a pizza chain to its holdings. The privately held Little Caesars is rumored to be for sale, but there are also opportunities in the public markets.

Rival fast food conglomerate Yum Brands! has seen disappointing results from its Pizza Hut chain, and analysts have wondered if the company would be open to selling the brand. Other top pizza chains, including both Domino's and Papa John's (NASDAQ:PZZA), are small enough to be acquired.

Both chains are highly committed to franchising, but from a growth perspective, Papa John's appears the more interesting target. It has less than half as many stores as Domino's, and about one-sixth as many international locations. Globally, the market for delivery pizza remains somewhat in its infancy, and Restaurant Brands could look to take an acquired pizza chain global.

Under new management
Burger King has been a fantastic investment since its public debut, and the acquisition of Tim Hortons has only strengthened the case for the company. Rather than a has-been burger chain trying to make a comeback, Burger King has morphed into an up-and-coming, international fast food conglomerate run by, perhaps, one of the best teams in the business.

Trying to front-run its next purchase may not be the wisest investment, but it does serve to highlight the case for Restaurant Brands.

Sam Mattera owns shares of Restaurant Brands International. The Motley Fool recommends Apple and Chipotle Mexican Grill. The Motley Fool owns shares of Apple, Chipotle Mexican Grill, and Papa John's International. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.