Marvin Gaye's Family -- Out for More Cash ... Targeting T.I.'s Pockets Now

Marvin Gaye's family didn't score enough in their "Blurred Lines" lawsuit -- now they're going after T.I. and a few record labels to pay up ... on top of the $7.4 million they won last week.

Only Pharrell and Robin Thicke were hit with the judgement last week, but attorneys for the Gaye family want Universal Music, Interscope Records and Star Trak Entertainment to fork over some cash too -- as well as T.I., who rapped on 'Blurred.'

Attaching the record labels could be the first step toward the family's other goal -- getting an injunction to stop distribution of the hit song until Marvin gets a writer's credit ... and, of course, the family gets royalties.