The integration of dissimilar materials in heterostructures has long been a cornerstone of modern materials science—seminal examples are 2D materials and van der Waals heterostructures. Recently, new methods have been developed that enable the realization of ultrathin freestanding oxide films approaching the 2D limit. Oxides offer new degrees of freedom, due to the strong electronic interactions, especially the 3d orbital electrons, which give rise to rich exotic phases. Inspired by this progress, a new platform for assembling freestanding oxide thin films with different materials and orientations into artificial stacks with heterointerfaces is developed. It is shown that the oxide stacks can be tailored by controlling the stacking sequences, as well as the twist angle between the constituent layers with atomically sharp interfaces, leading to distinct moiré patterns in the transmission electron microscopy images of the full stacks. Stacking and twisting is recognized as a key degree of structural freedom in 2D materials but, until now, has never been realized for oxide materials. This approach opens unexplored avenues for fabricating artificial 3D oxide stacking heterostructures with freestanding membranes across a broad range of complex oxide crystal structures with functionalities not available in conventional 2D materials.