Kate Upton and her boyfriend, former “Dancing With the Stars” hunk Maksim Chmer­kovskiy, continue to cuddle all around town.

The lovebirds were spotted at West Village eatery Hudson Clearwater, where our spy said they were “engaging in a lot of very, very heavy PDA. Maks was wearing a T-shirt that Kate had her hand down . . . like, through the neck hole.”

Page Six reported that Upton’s aiming to move to the Residences at W New York Downtown to be closer to her beau in the city.