Kinetics-controlled van der Waals epitaxy in the near-equilibrium limit by metal-organic chemical vapour deposition enables precise layer-by-layer stacking of dissimilar transition metal dichalcogenides. A broad range of transition metal dichalcogenide (TMDC) semiconductors are available as monolayer (ML) crystals, so the precise integration of each kind into van der Waals (vdW) superlattices (SLs) could enable the realization of novel structures with previously unexplored functionalities. Here we report the atomic layer-by-layer epitaxial growth of vdW SLs with programmable stacking periodicities, composed of more than two kinds of dissimilar TMDC MLs, such as MoS2, WS2 and WSe2. Using kinetics-controlled vdW epitaxy in the near-equilibrium limit by metal-organic chemical vapour depositions, we achieved precise ML-by-ML stacking, free of interlayer atomic mixing, which resulted in tunable two-dimensional vdW electronic systems. As an example, by exploiting the series of type II band alignments at coherent two-dimensional vdW heterointerfaces, we demonstrated valley-polarized carrier excitations-one of the most distinctive electronic features in vdW ML semiconductors-which scale with the stack numbers n in our (MoS2/WS2)(n) SLs on optical excitations.