A multiple-reaction irreversible surface reaction model involving one dimer and two different monomers (A and C) is proposed and studied by means of Monte Carlo simulations. This dimer - monomer - monomer (DMM) model is suitable to investigate, on the one hand, the influence caused by dimer traces on the behaviour of the monomer - monomer (MM) model, i.e. , and on the other hand, the effects of monomer traces on the dimer - monomer (DM) model, i.e. , which mimics the catalytic oxidation of carbon monoxide (B is O, A is CO and AB is CO). The DMM model exhibits irreversible phase transitions (IPTs) between poisoned states with the surface saturated by adsorbed species and reactive regimes with production of AB, AC and BC. The critical points at which second- and first-order IPTs take place are determined. Second-order IPTs belong to the universality class of directed percolation. However, universality is not found to hold at first-order IPTs due to short-range correlations. So, each critical point has its own set of critical exponents. These exponents smoothly cross over from values characteristic of the DM model to those of the MM model.