AdS4 backgrounds with N>16 supersymmetries in 10 and 11 dimensions

We explore all warped $Ad{S}_4{\times }_w{M}^{D-4}$ backgrounds with the most general allowed fluxes that preserve more than 16 supersymmetries in $D=10$- and $11$-dimensional supergravities. After imposing the assumption that either the internal space $M^{D-4}$ is compact without boundary or the isometry algebra of the background decomposes into that of AdS${}_4$ and that of $M^{D-4}$, we find that there are no such backgrounds in IIB supergravity. Similarly in IIA supergravity, there is a unique such background with 24 supersymmetries locally isometric to $Ad{S}_4\times {\mathbb{C}\mathbb{P}}^3$, and in $D=11$ supergravity all such backgrounds are locally isometric to the maximally supersymmetric $Ad{S}_4\times S^7$ solution.