Anonymous data within schools - how not to just use group mean over time - looking for references

I'm doing behavioral research and would like to research methodologies of dealing with a set of data. I have anonymous surveys from school staff from 40 schools (between 10-150 staff answering surveys at each school) at 4 timepoints. Scales based on likert scale items. I have some information on the surveys about gender, job type (teacher, admin, staff), but nothing to directly link surveys over time.
Schools are divided equally into intervention and control group. We might expect differences in scales by gender and job type also. We would be interested both in if there are baseline differences between groups and differences in change over time within groups. I want to see what others might have done statistically with data sets like mine (other than just using a group mean). Also, I have tried grouping by gender by job type (teacher vs everyone else), but especially in the smaller schools, I still have empty cells, so I'd have a smaller N comparing male, other staff than female, teachers, for example. I'd be interested if anyone has seen literature that examines working with this kind of data.