The medication should be taken 'under' a doctor's 'supervision'. = The medication should be taken 'under the supervision of' a doctor.
She's responsible for the 'supervision' of a large staff.
Young children need constant 'supervision'.
(..) know what's best for you. Don't let me see you in here again. Now, Margaret Sadovsky. I think some adult guidance, supervision... could benefit you too, young lady. Because you have no legal guardian-- Is that right? Yes. (..)1996 Foxfire