Transition-metal dichalcogenide (TMDC) homo- and heterostacks hold tantalizing prospects for being integrated as active components in future van der Waals (vdW) electronics and optoelectronics. However, most TMDC homo- and heterostacks are created by onerous mechanical exfoliation, followed by a mixing-and-matching process. While versatile enough for pilot demonstrations, these strategies are clearly not scalable for practical technologies and widespread implementations. Here, we report a two-step epitaxy strategy that promotes the growth of second-layer TMDCs on the basal plane of the first TMDCs epilayer. The first-layer TMDCs are grown on substrates where the tensile strength can be tuned by the control of chemical environments. The succeeding epilayers then prefer to grow layer-by-layer on the highly tensile-strained first layers. The result is the growth of high-density TMDC homo (WSe2) bilayers and hetero (WSe2-MoS2) bilayers with an exceedingly high yield (>99% bilayers) and uniformity. A density functional theory simulation further sheds light on how strain engineering shifts the subsequent layer growth preference. Second-harmonic generation and high-angle annular dark-field scanning transmission electron microscopy collectively attest to the AB and AA′ stacking between the TMDC epi- and overlayers. The proposed strategy could be a versatile platform for synthesizing diverse arrays of vdW homo- and heterostacks, thus providing prospects for realizing large-scale and layer-controllable two-dimensional electronics.