Maximal rank solution to $W^+Y = W^+WX$

Let $$X \in \mathbb{R}^{a \times n}$$ and $$Y \in \mathbb{R}^{b \times n}$$. How can we find a matrix $$W \in \mathbb{R}^{b \times a}$$ of maximal rank, such that $$W^+Y = W^+WX$$ (or alternatively, $$WW^+Y = WX$$) where $$W^+$$ denotes the pseudoinverse of $$W$$? We care about the $$W$$ of maximal rank, as one could trivially take $$W$$ to be all zeros and the equation would hold. From a geometric perspective, we're looking for a $$W$$ such that when $$X$$ is mapped to the column space of $$W$$, and $$Y$$ is mapped to the row space of $$W$$, these two images are equal when one considers the canonical isomorphism between the row and column space of $$W$$. In case it's necessary, we can assume that $$X$$ and $$Y$$ have full rank.