non-church 403(b) plan and ministerial housing

[JustMe]

We have a church that is not controlling over a school (of the same name and denomination) and the church's ministers teach in the school. The school wants to allow the ministers to contribute to the school's 403(b) plan and allow them to designate distributions as ministerial housing allowance. If the ministers' work qualifies as ministerial work for the school, can the school (and not the church) allow ministerial housing allowance designation or must the allowance come out of a church plan only?