We study theoretically the electronic transport in parallel few-level quantum dots in the presence of both intradot and interdot long-range Coulomb interaction. Each dot is connected to two leads and the steady-state currents are calculated within the Keldysh formalism using the random-phase approximation for the interacting Green functions. Due to the momentum transfer mechanism between the two systems it is possible to get a nonvanishing current through an unbiased Coulomb-blockaded dot if the other dot is set in the nonlinear transport regime. The transitions between the levels of the passive dot reduce the drag current and lead to negative differential conductance.