We investigate the energy landscape of an alchemical system of point particles in which the parameters of the interparticle potential are treated as degrees of freedom. Using geometrical optimization, we locate minima and transition states on the landscape for pentamers. We show that it is easy to find the parameters that give the lowest energy minimum and that the distribution of minima on the alchemical landscape is concentrated in particular areas. In contrast to the usual changes to an energy landscape when adding more degrees of freedom, we find that introducing alchemical degrees of freedom can reduce the number of minima. Moreover, compared to landscapes of the same system with fixed parameters, these minima on the alchemical landscape are separated by high barriers. We classify transition states on the alchemical landscape by whether they become minima or remain transition states when the potential parameters are fixed at the stationary point value. We show that those that become minima have a significant alchemical component in the direction of the pathway, while those that remain as transition states can be characterized mainly in terms of atomic displacements.