The low-energy band structure of few-layer MoS$_2$ is relevant for a large variety of experiments ranging from optics to electronic transport. Its characterization remains challenging due to complex multi band behavior. We investigate the conduction band of dual-gated three-layer MoS$_2$ by means of magnetotransport experiments. The total carrier density is tuned by voltages applied between MoS$_2$ and both top and bottom gate electrodes. For asymmetrically biased top and bottom gates, electrons accumulate in the layer closest to the positively biased electrode. In this way, the three-layer MoS$_2$ can be tuned to behave electronically like a monolayer. In contrast, applying a positive voltage on both gates leads to the occupation of all three layers. Our analysis of the Shubnikov--de Haas oscillations originating from different bands lets us attribute the corresponding carrier densities in the top and bottom layers. We find a twofold Landau level degeneracy for each band, suggesting that the minima of the conduction band lie at the $pm K$ points of the first Brillouin zone. This is in contrast to band structure calculations for zero layer asymmetry, which report minima at the $Q$ points. Even though the interlayer tunnel coupling seems to leave the low-energy conduction band unaffected, we observe scattering of electrons between the outermost layers for zero layer asymmetry. The middle layer remains decoupled due to the spin-valley symmetry, which is inverted for neighboring layers. When the bands of the outermost layers are energetically in resonance, interlayer scattering takes place, leading to an enhanced resistance and to magneto-interband oscillations.
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