Consider two categories $\mathbf A$ and $\mathbf B$. Assume that $\mathbf A$ is a small category. Then construct the functor category $[\mathbf A,\mathbf B]$, whose objects are all morphisms from $\mathbf A$ to $\mathbf B$ and whose morphisms are all natural transformations between such functors.
Then if $\mathbf B$ is a large category, $[\mathbf A,\mathbf B]$ is a proper metacategory in the sense that its objects or morphisms form not a class, but a conglomerate.
And it is known that this functor metacategory is legitimate; i.e., it is isomorphic to some category in usual sense.
But how can this situation be realized since metacategories and categories have different sizes?