Adhesion interactions mediated by multiple bond types are relevant for many biological and soft matter systems, including the adhesion of biological cells and functionalized colloidal particles to various substrates. To elucidate advantages and disadvantages of multiple bond populations for the stability of heterogeneous adhesion clusters of receptor-ligand pairs, a theoretical model for a homogeneous parallel adhesion bond cluster under constant loading is extended to several bond types. The stability of the entire cluster can be tuned by changing densities of different bond populations as well as their extensional rigidity and binding properties. In particular, bond extensional rigidities determine the distribution of total load to be shared between different subpopulations. Under a gradual increase of the total load, the rupture of a heterogeneous adhesion cluster can be thought of as a multistep discrete process, in which one of the bond subpopulations ruptures first, followed by similar rupture steps of other subpopulations or by immediate detachment of the remaining cluster. This rupture behavior is qualitatively independent of involved bond types, such as slip and catch bonds. Interestingly, an optimal stability is generally achieved when the total cluster load is shared such that loads on distinct bond populations are equal to their individual critical rupture forces. We also show that cluster heterogeneity can drastically affect cluster lifetime. © 2020 authors. Published by the American Physical Society.