Most metallurgical properties, e.g., dislocation propagation, precipitate formation, can only be fully understood atomistically but most phenomena and quantities of interest cannot be measured experimentally. Accurate simulation methods are essential but first-principles density functional theory (DFT) is prohibitively expensive while empirical interatomic potentials are rarely sufficiently accurate for alloys. Machine learning (ML) is emerging as an approach to create computationally-efficient atomistic potentials achieving near-DFT accuracy. Building on recent work on binary Al-Cu and ternary Al-Mg-Si, here a family of neural network potentials (NNPs) for Al alloys of Al-Cu-Mg and Al-Cu-Mg-Zn is developed and assessed using the Behler-Parinello formulation. Training of the potentials uses a robust set of metallurgically-relevant structures including intermetallic phases, stacking faults, solute/solute and solute/stacking fault interactions, solute clusters, and matrix/precipitate interfaces. The accuracy of these NNPs is then demonstrated across a comprehensive set of properties derived from the training set structures and, moreover, many important structures not represented in the training set such as the generalized stacking fault energy (GSFE) surface of the critical S-phase precipitate in Al-Mg-Cu, and antisite and vacancy formation energies for Al-Cu-Mg intermetallics. The broader Al-Cu-Mg-Zn NNPs also have high accuracy for subtle properties such as Cu substitutional energies in the n' and T phases and formation energies of small Al-Zn-Mg clusters. Together with earlier results, this paper shows how increasingly complex multicomponent alloy potentials can be systematically developed by expanding a training database, leading to a comprehensive set of potentials for a broad alloy family, demonstrated here for the technological Al-2xxx, Al-5xxx, and Al-7xxx Al alloys.