Lego, the undisputed construction toy king, has more than doubled its profits in the last five years and many of its sets are top sellers during the holiday season. Its success and the fact that it lost a long-running trademark battle over the interlocking brick in 2010 have encouraged competition.

Big toy makers like Hasbro, Mattel and Spin Master have also turned to construction toys to help bolster their sales. And smaller companies like the Bridge Direct, Cobi and OYO Sports have entered the field, putting more pressure on Lego. Interest in construction toys has even led to a secondary market of brick rentals.

Lego’s competitors say they want to distinguish themselves from their biggest rival. MEGA Brands, a subsidiary of Mattel and Lego’s closest rival, goes “above and beyond the squares and rectangles,” said Andrew Sparkes, vice president for global brand marketing at MEGA Brands.

“We are creating some of the most realistic sets out there,” he said, including sets based on the Halo video games and the movie “Terminator Genisys.” MEGA recently signed licensing deals for the classic “Star Trek” TV series and Teenage Mutant Ninja Turtles.

MEGA Brands was acquired by Mattel in 2014 in a deal that increased MEGA Brands’ worldwide distribution, said Gerrick Johnson, analyst for BMO Capital Markets. That global reach may have helped MEGA Brands secure licenses for brands like SpongeBob SquarePants and Teenage Mutant Ninja Turtles, because with a smaller company like MEGA Brands, “you might get more attention and innovation,” Mr. Johnson said.

Other companies are exploring themed sets that do not fit with Lego’s more wholesome brand.

“We have values in place that the brand is known for that we focus on,” said Michael McNally, brand relations director for Lego. “We don’t do military themes or anything overly violent or grotesque.”