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Electron ptychography is a powerful computational method for atomic-resolution imaging with high contrast for weakly and strongly scattering elements. Modern algorithms coupled with fast and efficient detectors allow imaging specimens with tens of nanometers thicknesses with sub-0.5 Ångstrom lateral resolution. However, the axial resolution in these approaches is currently limited to a few nanometers, limiting their ability to solve novel atomic structures ab initio . Here, we experimentally demonstrate multi-slice ptychographic electron tomography, which allows atomic resolution three-dimensional phase-contrast imaging in a volume surpassing the depth of field limits. We reconstruct tilt-series 4D-STEM measurements of a $\mathrm{Co_3O_4}$ nanocube, yielding 2 Å axial and 0.7 Å transverse resolution in a reconstructed volume of $\mathrm{(18.2\,nm)^3}$ . Our results demonstrate a 13.5-fold improvement in axial resolution compared to multi-slice ptychography while retaining the atomic lateral resolution and the capability to image volumes beyond the depth of field limit. Multi-slice ptychographic electron tomography significantly expands the volume of materials accessible using high-resolution electron microscopy. We discuss further experimental and algorithmic improvements necessary to also resolve single weakly scattering atoms in 3D.