In this talk we are in interested in the problem of a lifting a Kock-Zoberlein doctrine P to the 2-category of pseudo T-algebras for some pseudomonad T. Our main goal is to show that in this setting, one may recast the algebraic notion of a pseudo-distributive law in terms of size conditions and left extension properties. Moreover, due to the relationship with Yoneda structures noted earlier, we will also wish to consider the properties of a KZ-induced "Yoneda structure" in the presence of such a distributive law.