Master Calendar without using 3rd party calendar?

I’m the HR manager at a small non-profit. We’re looking for a master calendar that allows us to view the schedules of all employees, appointments, interviews, events, courses, etc. We are self-hosted, and for HIPAA reasons, we want to avoid using third-party calendars (google, ical) to keep client names secure.
Ideally, I would like to be able to see the schedules of my department heads in order to schedule their appointments. I would also like to be able to direct clients to a page of an employee’s open appointments that reflects their actual free time and not conflict with existing events.
Additionally, I would like employees and volunteers to be able to see days/times in need of coverage and to be able to schedule themselves to work those times.
Is this something possible within ERPNext?