  Amongst a number of modified theories of gravity, the Rastall theory has been
propounded to address some shortcomings of the standard theory of general
relativity. Our purpose is to investigate this framework's capacity to analyse
stellar structure in the context of elementary requirements for physical
plausibility such as positive definite functions for the energy density and
pressure, conformity to the causality criterion and the existence of an
equation of state. We consider the analogue of the Saslaw \textit{et al}
\cite{saslaw} isothermal model of general relativity and show that the Rastall
version satisfies the basic requirements unlike its counterpart. Then we
examine in turn the consequences of suppressing one of the inverse square law
fall off of the energy density or the linear equation of state. In addition,
the case of a constant spatial gravitational potential is studied on account of
this prescription being a necessary and sufficient condition for isothermal
behaviour in Einstein theory and its most general tensor extension Lovelock
gravity.
