Studies of multiphase fluids utilizing the lattice Boltzmann method (LBM) are typically severely restricted by the number of components or chemical species being modeled. This restriction is particularly pronounced for multiphase systems exhibiting partial miscibility and significant interfacial mass exchange, which is a common occurrence in realistic multiphase systems. Modeling such systems becomes increasingly complex as the number of chemical species increases due to the increased role of molecular interactions and the types of thermodynamic behavior that become possible. The recently introduced fugacity-based LBM [Soomro et al., Phys. Rev. E 107, 015304 (2023)2470-004510.1103/PhysRevE.107.015304] has provided a thermodynamically consistent modeling platform for multicomponent, partially miscible LBM simulations. However, until now, this fugacity-based LB model had lacked a comprehensive demonstration of its ability to accurately reproduce thermodynamic behavior beyond binary mixtures and to remove any restrictions in a number of components for multiphase LBM. In this paper we closely explore these fugacity-based LBM capabilities by showcasing comprehensive, thermodynamically consistent simulations of multiphase mixtures of up to ten chemical components. The paper begins by validating the model against the Young-Laplace equation for a droplet composed of three components. The model is then applied to study mixtures with a range of component numbers from one to six, showing agreement with rigorous thermodynamic predictions and demonstrating linear scaling of computational time with the number of components. We further investigate ternary systems in detail by exploring a wide range of temperature, pressure, and overall composition conditions to produce various characteristic ternary diagrams. In addition, the model is shown to be unrestricted in the number of phases as demonstrated through simulations of a three-component three-phase equilibrium case. The paper concludes by demonstrating simulations of a ten-component, realistic hydrocarbon mixture, achieving excellent agreement with thermodynamics for both flat interface vapor-liquid equilibrium and curved interface spinodal decomposition cases. This study represents a significant expansion of the scope and capabilities of multiphase LBM simulations that encompass multiphase systems of keen interest in engineering.