Is Robert Pattinson romancing both his co-stars?

Could the vampire hottie really be this much of a Casanova?

In Vancouver to film the Twilight sequel New Moon, Robert Pattinson's been spending his evenings sneaking between two different hotel rooms — Kristen Stewart's and Nikki Reed's.

Rob isn't staying at the same hotel (he's in a secret location to keep the crazed fans away) but he's been spending almost every night in the room of at least one of his co-stars.

"He often arrives late and leaves early in the morning, so we all know he's hooking up with one of them," a source tells Star magazine.

"He charges coffee to a suite on the ninth floor, where Nikki has a room," adds the source. But apparently when Nikki was away for a few days Rob's visits to the hotel continued… only this time he was hitting the twelfth floor, where Kristen is staying.

Rob's co-stars have said they're not interested in him romantically, but who knows what they're really up to?

"The girls are competing for Rob's attention," the source tells Star. "Kristen and Nikki both like him, and it's getting ugly. They're headed for a major showdown!"