I probably will run into a risk of this question being considered inappropriate for this forum. Still keeping fingers crossed!
One knows that given a classical system, if it is quantized in two different methods by say differing them in the ordering (normal ordered and anti-normal ordered) then the quantum spectrums one will get will differ only by a "constant".
I don't know how to make this notion of "quantizing in two different ways" precise except when one can distinguish them by just ordering.
But shouldn't it be possible that having quantized a classical system in two different methods in general it should be possible that their "classical limits" are actually different classical systems?
If the above is true then can one give some simple examples where this can be seen?