New parents Cox and David Arquette launch a new company, Coquette

First came a baby for Courteney Cox and David Arquette – daughter Coco, born June 13 – and now, the couple are stepping up their output with a new production company.

The actors have launched a company they’re calling Coquette, and the former Friends star has signed a first-look deal with Warner Bros. TV, the production company behind her hit sitcom (and which, like PEOPLE, is part of Time Warner), according to the Hollywood Reporter.

Among the projects Coquette reportedly has in development: The Fall and Rise of Taylor Kennedy, a drama with HBO interest that would star Cox and have Nick Cassavetes writing and directing; Dirt, a drama for FX; and Midnightly News, an unscripted half-hour comedy, which is expected to be sold to FOX.

“It is a natural progression for us, at this stage in our careers, to be moving toward development and production in both television and film,” Cox, 40, tells the trade paper.

The couple made their TV series producing debut with Mix It Up, a home-decorating show for WE: Women’s Entertainment, co-hosted by Thea Mann, a former casting agent who will serve as Coquette’s head of development.

“We got our feet wet with … Mix It Up, which is going into its second season and enjoyed that process so much we decided to formalize our commitment by forming this company,” says Arquette, 32.