Understanding the correlations between liquids and solids opens the way to predict by investigating liquids, the domains of thermodynamic parameters favoring intriguing solid phases. This approach is especially urgent for the design of multicomponent systems working with a continuous array of component concentrations (most modern materials of practical interest are multicomponent). Here we address an Al-Cu-Co system experimentally and theoretically using molecular dynamics and machine learning interaction potentials on top of the first-principles training data in a composition range of 15 at.% Co and 10 to 30 at.% Cu, and 25 at.% Cu and 2.5 to 20 at.% Co. The selected concentration sections contain different high-temperature solid phases. Differential thermal analysis has uncovered the features of solid phase formation at slow cooling and normal pressure. The boundaries of different phase regions correlate with the extrema on the one hand in undercooling and on the other hand in viscosity in the concentration area. The theoretical calculations have uncovered the correlations between the extrema and the readjustment of the chemical short-range order in the liquid, with the nonmonotonicity of the concentration dependence of the glass transition temperature and the specific volume.