I am inclined to think it would be possible, though extremely unlikely. As Cmwinters and Stubbornly Appeared pointed out, anyone changing subjects after the first term or two of third year is going to have masses to catch up with. Most students wouldn't be able to cope with that sort of self-study and catching up, but there are exceptions. I think people of Hermione and Percy's ilk (Rather than James and Sirius, say) would be able to put in the necessary reading to catch up, eventually.
Of course even students of that caliber would be at a huge disadvantage, so I think the circumstances for changing subjects would have to be fairly extreme. I don't think a dislike of it or an argument with the teacher (however severe) would cut it. I think we're talking about a Divination 3rd year in OotP, who is allergic to Centaurs. That kind of thing. So possible, but not greatly plausible.
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Gordon Owen and the Eastern Warrior; chapter 7 up!!!
I draw.
"Everything will be die."[sic] - Gallhammer
Remember kids, Snape didn't kill Dumbledore, Michael Gambon did.
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