In our recent study we showed that single component emulsion drops, stabilized by proper surfactants, can spontaneously break symmetry and transform into various polygonal shapes during cooling [Denkov et al. Nature 2015, 528, 392-395]. This process involves the formation of a plastic rotator phase of self-assembled oil molecules beneath the drop surface. The plastic phase spontaneously forms a frame of plastic rods at the oil drop perimeter which supports the polygonal shapes. However, most of the common substances used in industry appear as mixtures of molecules rather than pure substances. Here we present a systematic study of the ability of multicomponent emulsion drops to deform upon cooling. The observed trends can be summarized as follows: (1) The general drop-shape evolution for multicomponent drops during cooling is the same as with single-component drops; however, some additional shapes are observed. (2) Preservation of the particle shape upon freezing is possible for alkane mixtures with chain length difference Delta n <= 4; for greater Delta n, phase separation within the droplet is observed. (3) Multicomponent particles prepared from alkanes with Delta n <= 4 plastify upon cooling due to the formation of a bulk rotator phase within the particles. (4) If a compound, which cannot induce self-shaping when pure, is mixed with a certain amount of a compound which induces self-shaping, then drops prepared from this mixture can also self-shape upon cooling. (5) Self-emulsification phenomena are also observed for multicomponent drops. In addition to the three recently reported mechanisms of self-emulsification [Tcholakova et al. Nat. Commun. 2017 (8), 15012], a new (fourth) mechanism is observed upon freezing for alkane mixtures with Delta n > 4. It involves disintegration of the particles due to a phase separation of alkanes upon freezing.