A cluster supersymmetry scheme based on a core+α configuration is applied to nuclei with mass numbers A = 20, 19 and 18. The bosonic sector of the superalgebra of the model describes the relative motion of the clusters, while its fermionic sector is associated with the internal structure of the core. In the application considered, the core is a p-shell nucleus, leading to an underlying superalgebra U(4|12). For each of the six nuclei included in the analysis, the best-known α-cluster bands are considered. To gauge the validity of the supersymmetry approximation, electric quadrupole transition rates and one-nucleon transfer intensities are computed in two different ways: first for each nucleus separately and then jointly for the six nuclei. The analysis of the experimental data confirms the approximate validity of the U(4|12) supersymmetry for the six nuclei considered here.