The multiplicity features of integral catalytic reactors are studied numerically for the noble metal catalyzed oxidation of carbon monoxide with oxygen. The kinetics of the reaction are described with an elementary step model, displaying so-called kinetically induced rate multiplicity for certain conditions, i.e. multiplicity purely caused by the kinetics of the elementary steps. Implementation of the kinetic model requires separate continuity equations for the adsorbed species. An infinite number of steady states is predicted for an isothermal ideal plug how reactor, because ignition of the catalytic surface can occur at any axial position of the reactor. Superposition of axial back-mixing upon the plug flow as a feedback mechanism does not change this feature. If the reactor is operated in the region of kinetic multiplicity, an infinite number of steady states is also shown if heat conduction through the solid phase in axial direction is incorporated in the model. The latter is in contrast with previous studies of nonisothermal reactors. The only model extension leading to a finite number of steady states, i.e, five or three, in case of kinetic multiplicity is the introduction of a second-order space derivative in the continuity equation of the adsorbed species. The physical interpretation of the latter model extension is not clear however. For a nonisothermal reactor, the multiplicity source can change from purely kinetic to thermo-kinetic. The latter can result in a transition from a region with an infinite number of steady states to a region with a maximum of either three or five steady states. It is shown that the identification of the actual multiplicity source is important for a correct analysis of observed phenomena and that it is crucial for selecting an optimal operation strategy of industrial reactors.