If $apple$ is a valid unit then $apple^2$ is also a valid unit. Simply because it is valid does not imply that it is meaningful. 

Whether or not a unit is meaningful has to do with whether it is used in any physical formulas. I don’t know of any formulas that involve the unit $apple$, nor any that take products of quantities measured in $apples$. So to my knowledge it is not meaningful. 

If there were such a formula then the meaning of the unit $apple^2$ would be as a reference standard for the quantity described by the corresponding variable in the formula. 

You cannot talk about the meaning of a unit in the absence of a physical formula using that unit. For example the unit $\text{kg m}^2 \text{ s}^{-2}$ means different things in different contexts.