I've been trying to realise the full consequences of adding a series Rz and Cz to the output of the first stage of an output-pole compensated opamp.

Clearly we get a zero at the frequency given by the zero cap and res (call Rz and Cz here). But I'm trying to figure out a full analysis of how the poles are determined. Given that this is an output pole compensated amp, i want to keep the cap as low as possible, and the poles high in frequency.
My analysis so far has gone like this, and has yielded few insights:


Clearly we get a zero at the frequency given by the zero cap and res (call Rz and Cz here). But I'm trying to figure out a full analysis of how the poles are determined. Given that this is an output pole compensated amp, i want to keep the cap as low as possible, and the poles high in frequency.
My analysis so far has gone like this, and has yielded few insights:
