Use 2 moodle installations, M1 and M2. M1 will serve as the LTI tool, M2 as the platform.

In M1: goto Site Admin-Plugins-Enrolments-Publish as LTI tool-tool registration. Register M2 as a platform.

In M1: add three courses, and add an LTI advantage 'Publish as LTI-tool'  for each of them.

In M2: goto Site Admin-Plugins-Activity Modules-External tools-Manage tools. Copy the registration url from M1 into the "Add tool"-textbox and click "Add LTI advantage".
Activate the new external tool (wait for the registration to complete by checking in M1)

In M2: create a new course and add three external tools. Choose the preconfigured tool and add the respective "id=......." in each field "Custom parameters".

In M2: create a new user "Noob" and enrol this user as a student in the freshly created M2 course.

Login as Noob in M2 and got the course.

Click on the first external tool. Result: a new user is created automatically and enrolled in the first course in M1.

Click on the second external tool in M2. Result: the user is redirected to the first course in M1. No enrolment in the second course occurs.

Manually add the user in the second cours in M2.

As Noob in M1, click on the first and second, both links redirect to the correct course in M2.

As Noob in  M1, click on the thrid external link, the user is enrolled in the third course in M2.