We study a dimer-trimer lattice model for heterogeneous catalysis for the reaction 1/2A_2 + 1/2B_3 -> AB. The A_2 and B_3 particles require two and three active sites for their adsorption onto the lattice, respectively. The model is unusual in that it possesses an infinite number of absorbing states whereby the lattice is "poisoned" and reactions must stop. Previously studied models have only two absorbing states. In one dimension, the lattice poisons with mostly dimers and a few trimers even at vanishingly small dimer-adsorption probabilities and there is a discontinuity when this probability is zero. On the triangular lattice, the poisoned phases consist of only one component and vacancies, and the phase diagram is similar to that of the monomer~timer model of Ziff, Gulari, and Barshad. However, the second-order transition belongs to a different universality class than Reggeon field theory, contrary to previous models. Finally, we present results for the Kagom~ lattice, for which the poisoned phases consist of two components due to its smaller connectivity.