Plasma is often described as a separate phase of matter. The defining property of plasmas are they they are gases of freely moving charged particles, allowing large scale electric and magnetic phenomena to dominate their behavior. One of the ways that we pick out phase transitions is to look at how the temperature varies with input heat (heat capacity), with transitions occurring when the energy is going into driving a phase transition instead of increasing the kinetic motion in the medium (e.g. driving water molecules out of the liquid phase when boiling water).
With that in mind, if I take gas made of atoms of a single element (for concreteness, say carbon or oxygen) and proceed to heat it, does it exhibit a phase transition of the sort described above between ionization states? If so, are those ionization states considered separate phases, or some kind of "sub-phases" like the different phases in solid ice?
If no phase transition between ionization states occurs, then does that mean there is also no phase transition between neutral gas and plasma? If there is, then what separates that first ionization transition from the remaining ones?