In recent years the catastrophe theory, and in particular the singularity theory, has been utilized for analysing the multiplicity problem of a Continuous Stirred Tank Reactor (CSTR) caused by bifurcation of the equilibrium point due to a change in parameter values. Some important results, such as the existence of the winged cusp point, were obtained. In these works, the bifurcation of the equilibrium point due to the change in a single control parameter, such as the feed flow rate or the mean residence time, was investigated. Also, the fixed-parameter space was divided into subsets characterized by different bifurcation modes. In the present work, the heat transfer coefficient is added to the feed flow rate as another control parameter and the bifurcation set of the equilibrium point in the two-dimensional control-parameter space is determined. In consequence, the dimension of the fixed-parameter space is reduced by one and the classification of the bifurcation modes in the fixed-parameter space is greatly simplified. A clearer insight into the multiplicity problem is obtained, together with some new results.