The Joule-Thomson inversion curve (JTIC) separates regions in which heating and cooling occur upon an isenthalpic expansion. Mixture JTIC calculation is a clear matter for single-phase conditions; if the mixture splits in two or more equilibrium phases, derivatives properties are not defined. However, in practice a system may change its state during an isenthalpic expansion (i.e., a phase boundary is crossed between initial and final conditions); such situations are not uncommon in petroleum engineering applications. Recently, several JTIC construction procedures were proposed for two-phase vapor-liquid systems (D.V. Nichita, C.F. Leibovici, Calculation of Joule-Thomson Inversion Curves for Two-Phase Mixtures, Fluid Phase Equilibria 2006, 246, 167-176). For multiphase systems, an apparent JT coefficient can be defined, which incorporates both JT effects and phase distribution changes effects. In this work we present a method for JTIC calculation in multiphase systems, based on isenthalpic flash calculations, with emphasis on mixtures with solid-phase precipitation. Effects of the presence of a solid phase on the JTIC can be very important, since wax precipitation may occur in natural hydrocarbon systems (crude oils and gas condensates) at temperatures as high as 350 K. For multiphase systems, the locus separating heating/cooling regions in the temperature-pressure plane may have several distinct branches, corresponding to extrema of isenthalpic curves and to angular points of enthalpy variations (given by discontinuities in the JT apparent coefficient at phase boundaries). The proposed method is applied to JTIC calculations for several ternary mixtures and a synthetic hyperbaric fluid.