On the non-traditional end, the company is in talks with Six Flags theme parks about a possible partnership, said Nigel Travis, Papa John's president and chief operating officer. Expansion into urban areas will help the company grow in markets like Chicago, Detroit and Los Angeles, he said, as well as Philadelphia, where the firm recently bought out 15 franchises and plans to open 20 new units within the next four to five years. "We believe this new initiative can help us penetrate certain markets that have been very difficult for us," Travis said.

Internationally, Papa John's will focus on continued growth in China, India, Mexico, South Korea and the United Kingdom. Executives expect China, with 27 units, to grow to well beyond 400 restaurants. The pizza chain is also looking to expand its pipeline in Russia and other Eastern European countries. Meanwhile, the company is looking to sell a separate, 181-unit, UK-based chain called Perfect Pizza that it owns and franchises.

Domestic year-over-year same-store sales during the fourth quarter, which ended Dec. 25, were up 6.4%, with company-owned units rising 9.9% and franchised restaurants increasing 5.5%. Papa John's owns about 20% of its stores and franchises the remainder.