In standard supersymmetric (SUSY) models, the particles come in fermion–boson pairs. In spite of the expected abundance of super-partners for all known particles, not a single SUSY pair has been reported to date. Although a hypothetical SUSY breaking mechanism, operating at high energy inaccessible to current experiments cannot be ruled out, this reduces SUSY’s predictive power and it is unclear whether in its standard form SUSY can help reducing the remaining puzzles of the standard model (SM). We argue that SUSY can be realized in a different way, connecting spacetime and internal bosonic symmetries, combining bosonic gauge fields and fermionic matter particles in a single gauge field, a Lie superalgebra-valued connection. In this unconventional representation, states do not come in SUSY pairs, avoiding the doubling of particles and fields, and SUSY is not a fully off-shell invariance of the action. In addition, fermions are in the fundamental representation and bosons in the adjoint representation of the gauge group; their couplings follow the usual rules of the Standard Model; and SUSY is a symmetry of certain BPS vacua, not an invariance of the action.