updated 12/10/2010 AT 9:45 AM ET
•originally published 12/10/2010 AT 9:00 AM ET
The pair, along with the rest of the film’s cast, are now filming Breaking Dawn in Baton Rouge, La., after a stop in Brazil, and have been seen getting cozy around the southern city.
Pattinson, 24 and Stewart, 20 recently joined about two dozen other cast members for a private dinner at Fleming’s Prime Steakhouse and Wine Bar, but seemed to only have eyes for one another.
“Kristen and Rob were very couple-like,” a restaurant source tells PEOPLE. “There was a lot of hand-holding, sitting next to each other. Everyone was talking around the room, but Kristen and Rob were just talking to each other, not really into the conversations everyone else was having.”