  We conduct magnetic spherical Couette (MSC) flow experiments in the return
flow instability regime with GaInSn as the working fluid, and the ratio of the
inner to the outer sphere radii $r_{\rm i}/r_{\rm o} = 0.5$, the Reynolds
number ${\rm Re} = 1000$, and the Hartmann number ${\rm Ha} \in [27.5,40]$.
Rotating waves with different azimuthal wavenumbers $m \in \{2, 3, 4\}$
manifest in certain ranges of ${\rm Ha}$ in the experiments, depending on
whether the values of ${\rm Ha}$ were fixed or varied from different initial
values. These observations demonstrate the multistability of rotating waves,
which we attribute to the dynamical system representing the state of the MSC
flow tending to move along the same solution branch of the bifurcation diagram
when ${\rm Ha}$ is varied. In experiments with both fixed and varying ${\rm
Ha}$, the rotation frequencies of the rotating waves are consistent with the
results of nonlinear stability analysis. A brief numerical investigation shows
that differences in the azimuthal wavenumbers of the rotating waves that
develop in the flow also depend on the azimuthal modes that are initially
excited.
