I was in this situation at my previous school and it was an absolute nightmare. We weren't allowed to take anything away or do consequences of any kind. We were instructed to call home. 99% of the time, the parents either didn't care about the behavior/didn't see the behavior as a problem, or also had concerns at home but either couldn't or wouldn't address them.
Although they said we were a "PBIS school" we also didn't really have any rewards or tickets, etc. set up either. We weren't allowed to call the office unless a child was physically violent with someone. I once had a child screaming obscenities in someone else's face and knocking supplies off of their desk, and was chastised for calling the office. P said the problem was that my math lesson wasn't engaging enough
Basically admin were idiots who had no idea how PBIS or management of any kind worked.
I tried to do things within my own classroom to deal with this. At one point, I was doing a 5 minute game at the end of each subject (the game would be academic focused, like a word bingo or some type of math facts game, etc. ) that students had to earn through good behavior in the lesson. Unfortunately we had very frequent walkthroughs and my admin found out and made me quit doing even that
My current school does the PBIS/restorative justice stuff too, but admin does recognize that there is a point where you simply can't just do a "make it right." They also don't let a child's feelings/mood excuse terrible behavior. I remember one of the first days of last school year when new admin had started, AP was out talking to one of our "high flyers" in the hallway and he said something like, "I don't care if you don't like music class. You don't speak to any teacher like that" and I wanted to stand up and clap. Previous admin would have gone into a long conversation trying to figure out the feelings behind the child's dislike of music class
Our consequences include:
-Recess academy- students practice whatever routine they need to work on, such as walking in the hallway, sitting quietly, raising their hand, etc. In more severe cases this is with admin.
-Any aggression, property destruction, or unauthorized leaving the room/building is an automatic suspension. Students may not return to school without a "reentry" meeting with their parents where a plan for home and school behavior is discussed.
-Taking away field trips, field day, special assemblies, other "fun" activities
-Not receiving our "smart tickets" which are required for certain activities and privileges
-Admin does work diligently to make sure that the most extreme cases are moved to self-contained affective needs settings. Earlier this year, I had a kid that to make a long story short, had insane behaviors. Admin bypassed all of the hoops to get him moved by telling all of the district bigwigs that we needed help and that they needed to come observe/tell her what she needed to be doing better with this child. They came and we received an email within an hour stating he would be moved.
I'm in a very low SES school and I will say behavior is still a big issue that we're all dealing with on a daily basis. However, at least I feel that current admin is actually supporting us and working alongside us with the behavior rather than just implying that teachers need better management.