Magnetism in the Zintl compound Ba14MnBi11 is rather poorly understood. Experimental claims are largely inconsistent with ab initio calculations, much beyond typical errors of the latter. We revisit this old problem, assuming that the root of the problem may be in nonstoichiometry of existing samples. Our key finding is that the magnetic ground state is indeed very susceptible to charge doping (band filling). Calculations for stoichiometric Ba14MnBi11 give a rather stable ferromagnetic metallic state, in agreement with previous publications. However, by adding exactly one electron per Mn, the system becomes semiconducting as expected, and becomes weakly antiferromagnetic (AF). On the other hand, upon small amount of hole doping, the system transitions to a special type of AF state known as altermagnetism. Furthermore, hole and electron doping-induced phase transitions result from different underlying mechanisms, influencing different exchange pathways. We propose that the inconsistency between experiment and theory is not a failure of the latter, but results from a nontrivial ramification of nonstoichiometry. The possibility of doping-stabilized altermagnetism is exciting.