From the abstract for Alberto Gonzales, Presidential Powers, Immunities, and Pardons, 96 Wash. L. Rev. 1 (2018):
This Article intends to clarify some of the more difficult legal issues in our nation’s separation of powers jurisprudence. In order to afford the President the flexibility and discretion necessary to discharge presidential duties, the courts are almost certainly going to recognize total immunity from the criminal process for the President with respect to official conduct. The treatment of unofficial conduct is less predictable. Based on precedent and our nation’s founding principles of equal justice and fairness, the courts are likely to hold that a sitting President is not above the law and thus does not enjoy immunity from criminal prosecution for unofficial acts or conduct unrelated to his or her fitness to hold office. However, because of separation of powers considerations, the courts are likely to require deferral of any such prosecution until the President no longer holds office.
Although not as clear, constitutional considerations would likely also require deferral of any investigation or indictment, at least those requiring the direct and material participation of the President. On the other hand, the President can be compelled to produce certain documentary evidence when doing so is necessary and would otherwise be unavailable in connection with a criminal investigation. The argument for presidential immunity with respect to production of evidence is stronger, though likely not absolute, with respect to oral testimony. Nonetheless, mindful of the President’s duties, the courts are likely to afford the President great latitude in the time, place, and manner of providing oral testimony. Finally, there is nothing in the Constitution that expressly prohibits or limits the President from issuing a self-pardon.