Wordpress Plugin/Solution to Bridge Moodle and Rocketchat Logins

I need a Wordpress plugin or other solution that: 1) User signs up on Wordpress 2) User's information from register also registers an account on one or more Moodle LMS's (could be one, could be several) 3) User's information from register also registers an account on rocket chat. 4) User can click a link on the Wordpress to directly login and navigate to their page on either one of several Moodles, or rocket chat. To be clear, there will be a dynamic number of Moodles the user can access so it would be best for me, as the admin, to be able to just type in the Moodle database/information and add them to the Wordpress in a list. It would simplify things, and allow growth. Users will be added as a user for every Moodle on the list. There is only one rocket chat and it would be good if I could also enter the rocket chat information on the Wordpress in case there is a server or IP change. User signs up for Wordpress using a customized form and then is automatically registered on any listed Moodles and the rocket chat. I'd prefer each one to be separate plugins, as to modularize any necessary updates.