Director/co-screenwriter Karen Morey and co-screenwriter/star Terence Chen wanted to make a romantic comedy about romantic comedies, a meta-story that nods to many of the most beloved classics in the genre, from “Roman Holiday” to the oeuvre of Richard Curtis. In “Meet Cute in Manhattan,” the movie within the movie has a couple named Jason and Nora in a classic rom-com situation. They audition for a dating app commercial by pretending to be in love when they’ve just met and are in relationships with other people.