Set the payment processor callbacks to a plugin

We need for our Wordpress page a plugin which processes in certain situations the payments independently from the regular check-out page. Normally, a payment processor like PayPal, Stripe and others, use callback URLs to inform the site about the result.

So, we have now this situation:

The plugin needs to know the result of the payment process but the callback URLs are set to some URL which do not belong to the plugin. With other words, we would have 2 check-out pages.

My question:

Is there a general way how this plugin can catch/get the result of any payment and evaluate the result only then, when the payment was initiated by the plugin?