  Topological materials often exhibit remarkably linear, non-saturating
magnetoresistance (LMR), which is both of scientific and technological
importance. However, the role of topologically non-trivial states in the
emergence of such a behaviour has eluded clear demonstration in experiments.
Here, by reducing the coupling between the topological surface states (TSS) and
the bulk carriers we controllably tune the LMR behavior in Pt1-xAuxLuSb into
distinct plateaus in Hall resistance, which we show arise from a quantum Hall
phase. This allowed us to reveal how smearing of the Landau levels, which
otherwise give rise to a quantum Hall phase, results in an LMR behavior due to
strong interaction between the TSS with a positive g-factor and the bulk
carriers. We establish that controlling the coupling strength between the
surface and the bulk carriers in topological materials can bring about dramatic
changes in their magnetotransport behavior. In addition, our work outlines a
strategy to reveal macroscopic physical observables of TSS in compounds with a
semi-metallic bulk band structure, as is the case in multi-functional Heusler
compounds, thereby opening up opportunities for their utilization in hybrid
quantum structures.
