Based on high-throughput density functional theory calculations, we performed screening for stable magnetic MAB compounds and predicted potential strong magnets for permanent magnet and magnetocaloric applications. The thermodynamical, mechanical, and dynamical stabilities are systematically evaluated, resulting in 21 unreported compounds on the convex hull, and 434 materials being metastable considering convex hull tolerance to be 100 meV/atom. Analysis based on the Hume-Rothery rules revealed that the valence electron concentration and size factor difference are of significant importance in determining the stability, with good correspondence with the local atomic bonding. We found 71 compounds with the absolute value of magneto-crystalline anisotropy energy above 1.0 MJ/m$^3$ and 23 compounds with a uniaxial anisotropy greater than 0.4 MJ/m$^3$, which are potential gap magnets. Based on the magnetic deformation proxy, 99 compounds were identified as potential materials with interesting magnetocaloric performance.
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