I have a dataset with the following data-structure:

Across five school districts, students (N = 1000) are nested in teachers (n = 70). However, within school districts, each student can be nested in several teachers simultaneously. My dependent variable is students' wellbeing, and I would like to model the effect of student-level socioeconomic status and teacher-level job experience on differences in wellbeing.  Would you agree that a multilevel multiple membership model (with students nested simultaneously in teachers) might be best suited to this data structure?

In addition, I also have characteristics of the five school districts. Any ideas if (and if so, how) school district variables might be included into the model?

Many thanks for your suggestions and regards,