Call TYPO3 plugin from other plugin's body by cObject

Question

I've injected plugin in the template to display specific data from the controller and it works fine. But now I have to make an AJAX call to receive some records based on the select filter from this specific plugin. I wanted to inject second plugin into this first plugin to the template to make a possibility to return data as a partial template to the frontend.

This is a typoscript file:

lib.firstPlugin =< tt_content.list.20.first_p

In the template I use cObject to render this first plugin:

<f:cObject typoscriptObjectPath="lib.firstPlugin"/>

It is even possible? How I can send AJAX call to receive only partial template from the backend (in this case some records) to the first plugin. I used similar code as above for the second plugin and it doesn't work (AJAX call will always go to the first plugin and default controller method).

Thank you for potential tips.