The electric field in laser-driven plasma wakefield acceleration is orders of magnitude higher than conventional radio-frequency cavities, but the energy gain is limited by dephasing between the ultrarelativistic electron bunch and the wakefield, which travels at the laser group velocity. We present a way to overcome this limit within a single plasma stage. The amplitude of the wakefield behind a train of laser pulses can be controlled in-flight by modulating the density profile. This creates a succession of resonant laser-plasma accelerator sections and nonresonant drift sections, within which the wakefield disappears and the electrons rephase. A two-dimensional particle-in-cell simulation with four 2.5 TW laser pulses produces a 50 MeV electron energy gain, four times that obtained from a uniform plasma. Although laser redshift prevents operation in the blowout regime, the technique offers increased energy gain for accelerators limited to the linear regime by the available laser power. This is particularly relevant for laser-plasma x-ray sources capable of operating at high repetition rates, which are highly sought after.