The present paper analyzes three representative weakly compressible multiphase models. It is found that these models contain some identical numerical dissipation terms, i.e., pressure diffusion and bulk viscosity terms. Numerical investigations demonstrate that these identical numerical dissipation terms provide general mechanisms for stabilizing computations. The generality of mechanisms is reflected in (a) they widely exist in many weakly compressible multiphase models and (b) they are interpretable physical mechanisms that do not depend on numerical schemes. Many weakly compressible multiphase models can be incorporated into a general theoretical framework based on the general mechanisms. Consequently, a general weakly compressible solver for multiphase flows (GWCS-MF) is proposed. It is derived from standard governing equations and can be applied to nonuniform meshes easily. Detailed numerical tests show that it can achieve good numerical stability and accuracy for challenging conditions (inviscid fluids, large density ratios, high Weber numbers, and high Reynolds numbers) and simulate complex interface evolution well. These good performances exhibit the advantages of GWCS-MF and further validate those general mechanisms.