We present MAESTROeX, a massively parallel solver for low Mach number astrophysical flows. The underlying low Mach number equation set allows for efficient, long-time integration for highly subsonic flows compared to compressible approaches. MAESTROeX is suitable for modeling full spherical stars as well as well as planar simulations of dynamics within localized regions of a star, and can robustly handle several orders of magnitude of density and pressure stratification. Previously, we have described the development of the predecessor of MAESTROeX, called MAESTRO, in a series of papers. Here, we present a new, greatly simplified temporal integration scheme that retains the same order of accuracy as our previous approaches. We also explore the use of alternative spatial mapping of the one-dimensional base state onto the full Cartesian grid. The code leverages the new AMReX software framework for block-structured adaptive mesh refinement (AMR) applications, allowing for scalability to large fractions of leadership-class machines. Using our previous studies on the convective phase of single-degenerate progenitor models of SNe Ia as a guide, we characterize the performance of the code and validate the new algorithmic features. Like MAESTRO, MAESTROeX is fully open source.