The Oscar-nomianted actress – who is already mom to a beloved two-year-old chocolate Labrador, Esmeralda – accompanied boyfriend Adam Schulman to Molly’s Mutts and Meows volunteer animal rescue center in West Hollywood on Saturday, where the couple checked out several pooches in need of forever homes.
Adam and Anne were particularly taken with a medium-sized mutt named Chuck.
“She said she had one dog and was looking to adopt a second one. Most of the conversation was about Chuck, and whether he’s good with other dogs, house-trained, mellow, things like that,” a tipster told PEOPLE.