In this work unique twisted bilayers of MoSe2 with periodic multiple stacking configurations and interlayer couplings were discovered in the narrow range of twist angles, 60± 3°, using ulra-low frequency Raman spectroscopy and first-principle theory. We showed that the slight deviation from 60° creates patches featuring all three high-symmetry stacking configurations (2H or AA′, AB′, and A′B) in one unique bilayer system. In this case, the periodic arrangement of the patches and their size strongly depend on the twist angle. Our first-principle modeling predicts significant changes in frequencies and intensities of low-frequency modes versus stacking and twist angle. Experimentally, the variable stacking and coupling across the interface are revealed by the appearance of two breathing modes, corresponding to the mixture of the high-symmetry stacking configurations and unaligned regions of monolayers. Only one breathing mode is observed outside the narrow range of twist angles. This indicates a stacking transition to unaligned monolayers with mismatched atom registry without the in-plane restoring force required to generate a shear mode. The variable interlayer coupling and spacing in transition metal dichalcogenide bilayers revealed in this study may provide a new platform for optoelectronic applications of these materials.