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The primary phase of the Earth's lower mantle, (Al, Fe)-bearing bridgmanite, transitions to the postperovskite (PPv) phase at Earth's deep mantle conditions. Despite extensive experimental and ab initio investigations, there are still important aspects of this transformation that need clarification. Here, we address this transition in (Al3+, Fe3+)-, (Al3+)-, (Fe2+)-, and (Fe3+)-bearing bridgmanite using ab initio calculations and validate our results against experiments on similar compositions. Consistent with experiments, our results show that the onset transition pressure and the width of the two-phase region depend distinctly on the chemical composition: a) Fe3+-, Al3+-, or (Al3+, Fe3+)-alloying increases the transition pressure, while Fe2+-alloying has the opposite effect; b) in the absence of coexisting phases, the pressure-depth range of the Pv-PPv transition seems quite broad to cause a sharp D" discontinuity (< 30 km); c) the average Clapeyron slope of the two-phase regions are consistent with previous measurements, calculations in MgSiO3, and inferences from seismic data. In addition, d) we observe a softening of the bulk modulus in the two-phase region. The consistency between our results and experiments gives us the confidence to proceed and examine this transition in aggregates with different compositions computationally, which will be fundamental for resolving the most likely chemical composition of the D" region by analyses of tomographic images.