We study the effect of coadsorption of CO and O on a Ziff-Gulari-Barshad model with CO desorption for the reaction CO + O --> CO(2) on a catalytic surface. Coadsorption of CO at a surface site already occupied by an O is introduced by an Eley-Rideal-type mechanism that occurs with probability p, 0 < or = p < or = 1. We find that besides the well-known effect of eliminating the second-order phase transition between the reactive state and an O-poisoned state, the coadsorption step has a profound effect on the transition between the reactive state and the CO-poisoned state. The coexistence curve between these two states terminates at a critical value k(c) of the desorption rate k, which now depends on p. Our Monte Carlo simulations and finite-size scaling analysis indicate that k(c) decreases with increasing values of p. For p = 1, there appears to be a sharp phase transition between the two states only for k at (or near) zero.