My most recent school district had school behavioral health workers who were masters level people (masters in any number of fields- social work, counseling psychology, marriage/family therapy- most of the people in those positions had NO experience/training in working in schools) devoted to working with higher level needs including servicing behavioral goals on IEPs.
Most schools also had school counselors (although some were cutting those out) who primarily did group lessons in the classrooms and dealt with lower needs/crisis counseling. A huge part of their job description revolved around managing state testing and helping with scheduling.
At the district level, we also had a few clinical psychologists who were called in as the "big guns." They oversaw the school behavioral health workers, and they also provided some therapy to extremely high needs students.
And we had a few school psychologists who did some counseling/therapy, but were primarily seen as district assessors.
It seems like we had all levels covered, but the problems I saw revolved around communication and continuous service. The various branches almost never communicated with one another, and I saw that as very problematic. So kids who needed elevated services didn't seem to get that far, and lower service providers weren't aware of the kids receiving higher levels of services, so there was a lot of time lost because a "lower" service provider was trying to deal with a crisis that was actually an ongoing problem under treatment from the big guns. (lower here is just referring to the level of intense services given, NOT a reflection on my opinion of the providers!!

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