Is it always the same number of University´s that needs to be added to a Project?
If so, then you know the ID of for those UniversityID´s and can have a Script Trigger to run when you have created a new record in your Layout Settings. This script can take your Project ID in a Set Variable and then go to your ProjectToUniversity layout and create one record for each University
Your table looks like a join table linking many projects to many universities to many projects.
And I would then guess that guess that each time you add a new project record, you also want to add a new record to this table in order to link it to the current university record. Is that what you are doing?
Johan's method can be used to do that, but you will need a variable for both ID's.
There are other methods for doing this. Research "MagicKey" to find one such method.