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The quest towards expansion of the M_n+1AX_n design space has been accelerated with the recent discovery of several solid solution and ordered phases involving at least two M_n+1AX_n end members. Going beyond the nominal M_n+1AX_n compounds enables not only fine tuning of existing properties but also entirely new functionality. This search, however, has been mostly done through painstaking experiments as knowledge of the phase stability of the relevant systems is rather scarce. In this work, we report the first attempt to evaluate the finite-temperature pseudo-binary phase diagram of the Ti₂AlC-Cr₂AlC via first-principles-guided Bayesian CALPHAD framework that accounts for uncertainties not only in ab initio calculations and thermodynamic models but also in synthesis conditions in reported experiments. The phase stability analyses are shown to have good agreement with previous experiments. The work …