Multiple-phase disordered zeolites, i.e., intergrowth zeolites, are important industrial catalysts, like single-phase ordered zeolites, but little is known about their rational synthesis and phase competition, mainly due to current poor understanding of the zeolite crystallization mechanism. Here, we theoretically demonstrated that sodalite and cancrinite cage layers, the periodic building units (PerBUs) of FAU/EMT and SBT/SBS structures, respectively, could be nondefectively connected to each other across double rings of 6 tetrahedral atoms when inverted and mirrored. We then synthesized an unprecedented family of FAU/SBT/SBS intergrowths with controllable FAU portions (named as the PST-34 family of intergrowth zeolites) using a multiple inorganic cation approach, providing clear experimental evidence for the layer-by-layer crystal growth mechanism of zeolites. This study shows that control of interactive cooperation extent between different inorganic structure-directing agents in the presence of an unselective organic structure-directing agent may enable repeated stacking of different but structurally related PerBUs in intergrowth zeolite synthesis.