We propose an incremental construction of multi-timestep integrators to accelerate polarizable point dipole molecular dynamics while preserving sampling efficiency. We start by building various integrators using frequency-driven splittings of energy terms and a Velocity-Verlet evaluation of the most rapidly varying forces, and compare a standard dual bonded/non-bonded split to a 3-groups split dividing non-bonded forces (including polarization) into short- and long-range levels. We then introduce new approaches by coupling these splittings to Langevin Dynamics and to Leimkuhler's BAOAB integrator to reach larger timesteps of 6~fs for long-range forces maintaining accuracy. We further increase sampling efficiency by: i) accelerating the polarization evaluation using a fast/non-iterative Truncated Conjugate Gradient (TCG-1) as short-range solver; ii) pushing the outer timestep to 10~fs using hydrogen mass repartitioning. Finally, our Tinker-HP implementation of BAOAB-RESPA1-Langevin integrators demonstrates a 4 to 7-fold acceleration over standard 1~fs integration while preserving the evaluation of static and dynamical properties.