Adding custom data (API request / response) to logs

We are interested in using this plugin to capture API request and response data generated by user actions.

When our users register or update their profile the website make various create / update / read requests to a third party CRM and so we would like to capture the requests and responses along with the user action logs that the plugin looks like it would create anyway.

Is there a way that this can be done (happy with a native feature, custom coding using hooks etc)

Thanks
Sam