We study the effect of coadsorption of CO and O on a Ziff-Gulari-Barshad (ZGB) model with CO desorption (ZGB-d) for the reaction CO + O --> CO_2 on a catalytic surface. Coadsorption of CO on a surface site already occupied by an O is introduced by an Eley-Rideal-type mechanism that occurs with probability p, 0 <= p <= 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 strong 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 scale 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.