  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.
