We are a university enrolled in a Microsoft CASA (Campus and School Agreement). Our students and employees are licensed for the use of Office 365. Do the license terms allow the use of the software for private purposes as well?
Users licensed through a Microsoft Campus and School Agreement and who are not students are classified as “Education Qualified Users”. Such a user may only use the software for “the benefit of the institution”. Therefore, using the software for private purposes is not allowed.

Unfortunately, there is no explicit specification in the Product Terms when it comes to student users. This should make you vigilant because with Microsoft you should always assume that rights are only granted when they are described in the Product Terms. However, an organisation should look for legal protection and, for example, regulate the use of the software by letting the users sign an appropriate letter of intent.
Source: Microsoft Product Terms, March 2020