Abstract: The aim of this article is to predict possible invariant reactions in a quaternary system formed by oxides of titanium, aluminum, silicon, and zirconium. As a result, based on the data on invariant transformations in faceting ternary systems, a scheme of phase reactions with the participation of a liquid is derived, and then the contours of the liquidus hypersurfaces are described for basic invariant points belonging to binary and ternary systems, as well as the six obtained points of the quaternary system: two are peritectic, two are eutectic, and two are intermediate, corresponding to phase reactions of two variants of the peritectic type.