  Linear stability of Israel-Stewart theory in the presence of net-charge
diffusion was investigated in [Phys.~Rev.~D 102 (2020) 116009] for the case of
a massless, classical gas of noninteracting particles. However, in that work
only a vanishing net-charge background was considered. In this work, we extend
that study to the case of a nonvanishing background charge. We find that this
effectively results in a change of the numeric value of the charge-diffusion
coefficient, in a way that when the background charge goes to infinity, this
coefficient can become at most four times its value at zero background charge.
We also extend the analysis of [Phys.~Rev.~D 102 (2020) 116009] by performing a
systematic parameter study in the plane of charge-diffusion coefficient vs.\
the coupling term between shear-stress and net-charge diffusion. In this plane,
we identify regions where the solutions remain stable and causal and where they
become acausal and/or unstable.
