This work presents a trapping and diffusion model for multiple species of solute atoms in a system with multiple sorts of traps based on irreversible thermodynamics. We use two established approaches describing the interaction between lattice and traps, i.e. transient trapping and theory based local thermodynamic equilibrium, and extend them to systems with multiple species. Consequently, the presented theory and its numerical implementations cover effectively any kinetics of exchange between the lattice and traps as well as site competition effects within traps for any system size. The presented theory can be applied for several phenomena in material science. For example, (co-) segregation of solutes at grain boundaries, trapping of interstitials during precipitation processes and hydrogen interaction with material defects and other interstitials. Simulations of charging and discharging are presented for several plate-like samples containing multiple sorts of traps occupied by multiple species. The role of trapping parameters is demonstrated and discussed for charging and discharging behavior, site competition effects and the interaction of trapping kinetics with diffusion kinetics for multiple species.