Yes, private colleges and universities are treated as private corporations, and can both sue and be sued. However, universities or colleges which are public or semi-public can generally not be sued, unless state statute or the state legislature has authorized it.
Private universities can be sued for breach of contract, as can public universities when allowed by statute or the state legislature. However, in some states you may only make a breach of contract claim, or any claim, against a public university when it does not enjoy immunity.
There are conflicting views on this topic, so the answer will depend on which state you reside in. One view is that state school officials cannot be sued for their normal work activities. State employees are immune unless they acted outside of the scope of their responsibilities, or they acted with malicious purpose, bad faith, or in a reckless manner. Importantly, the immunity only protects the state employee if his or her conduct did not violate a clearly established statutory or constitutional right which a reasonable person would have known about.
Another view is that state school officials have qualified immunity as long as their actions were reasonable. This means that to have immunity the employee must be able to show that he or she was acting within the scope of his or her discretionary authority, and that he or she was acting in good faith. As with the first view mentioned, this immunity only protects against a state employee’s liability of his or her conduct did not violate a clearly established statutory or constitutional rights which a reasonable person would have known about.
You may wish to consult with an attorney to find out whether you are able to sue a college or university in your state. If you decide to file a lawsuit against the college or university, a government attorney will be essential to helping you navigate through the complicated legal system.