My suggestions, based on a system I set up a few years ago for schools (not universities):
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applicants are Leads
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actual students are Contacts
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Accounts are used to group students into classes and courses, with several levels (see multi-account belonging here: https://pgorod.github.io/Concepts-Accounts-Contacts/)
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Cases are also good to use for the enrollment process
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this didn’t include the school database of grades, that was a separate system. To do this in SuiteCRM would require a larger customization.
I recommend using some knowledgeable consultancy to migrate your data and get the concepts right, from the beginning. Tell me if you want to be contacted by SalesAgility about such a project. If not, just keep asking me questions here, and I will answer.