Unless half-time is the norm for this type of management postion, I think there is no doubt it's "substantially less favorable."
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You just have to figure out if you want to leave and whether you will be better off seeking another job. Yes, THEY CAN "Do It" to you. They can do a whole lot of things to you. But you have to figure out, do you want to work there, until you can find something better, or do you want to leave the job, go into the unemployment system and try to appeal and get an approved claim for unemployment, which will if approved, last a maximum of 26 weeks? If they offer you a job you don't want to take, go out and find yourself another job you do want to do, while you are still employed. That's something that would keep you working, keep you in the loop, and make you able to move on without a gap in your earnings. Yeah, if you don't want the supervisory job, you can quit, and you can appeal and see if you qualify for unemployment, but frankly, MOVE ON. That's the better way.
Seems to me you can get fired for refusing to undertake added tasks or duties under color of insubordination.
In some cases, not in your post, to add duties of management might convert the person from non exempt to exempt and result in a major pay cut....but that's not what you seem to describe .
but that's not what you seem to describe .
Then why are you bringing it up?