at my school, if you drop down to 10 or 11, you must get a signature from the head teacher of every subject you are currently doing. before they give you the signature, they look at your performance currently and if it is too low, they might strongly encourage you to keep the extra units as a safety net due to poor performance in subject X.
however, despite the warnings and all that, unless you're pretty much last, the head teachers will give you a signature.
after obtaining all these, then you have to go see deputy principal A - and explain your scenario and reasoning for dropping to 10 or 11. and properly discuss any concerns relating to it.... once the DP is fine with it, they will give their signature, and effectively you are now authorised to drop the units you wanted it.
so at my school as an example, although they do not control whether you drop to 10/11, they have a pretty big say. and after intense discussions with some kids, have knocked back a few students, declining to let them drop whatever they want.
whether the school is allowed technically to do this is another matter....