No, the moving of drawing views is not possible in Fusion 360 at this time.
John Hackney, Retired
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Will this feature be available in the near future?
I cannot speak for the developers at Autodesk as I am a Forum volunteer, just a user like yourself. You can look at the Fusion 360 Roadmap Update 2020 website and see what they are planning.
John Hackney, Retired
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There is a workaround, but it's kind of gross.
Perform a "save-as" and create a new copy of your drawing. Then you can delete what you don't want in each drawing.
Depending on your drawing number/sheet scheme this may cause you some headaches of its own, but hopefully less than trying to redo a bunch of work that you already put in.