In this work, a new level-set-based approach is presented and applied to compressible, multiphase flows. Using a species-mass-conservation-based level-set transport equation, several advantages over signed-distance-function- based methods are demonstrated. Specific improvements include a ghost-fluid-free method for highly compressible problems, extensions to an arbitrary number of specie, and finite-rate chemistry mass transfer modeling. While maintaining higher-order numerics, the approach is applicable to three-dimensional (3D), time-accurate/steady, turbulent simulations. Herein, the method is applied to a flow solver that fully couples the mass, momentum, energy, and level-set transport equation; although the methods are equally applicable to segregated flow solvers. The methods are tested for ventilated supercavities, natural cavitation (incompressible, compressible, and thermal), and shock-induced boiling. Lastly, new reinitialization methods are developed specific to cavitating flows that decrease the interface diffusion where needed, while retaining an ability to admit subgrid-scale mixtures. Such an approach enables a more physical solution method for certain classes of multiphase flows. This formulation of the level-set approach is a general, valid, method that could easily be incorporated into any species-mass conservation solver.