Sir Paul McCartney has taken his relationship with Nancy Shevell to the next level after reportedly beginning his hunt for an apartment nearer to her New York home.The former Beatle has been dating American heiress Shevell since last year and is now said to have made moves to purchase a property closer to her Upper East Side residence in the city.McCartney formerly owned a place in midtown Manhattan with ex-wife Heather Mills - who settled into her own apartment in the city's star-studded downtown West Village earlier this year.A source tells the New York Post, "He's been looking at eight-figure apartments. I think he just wants to rid himself of the Heather factor."