We generalize the standard first-order intertwining relationship of supersy
mmetric quantum mechanics in order to include simultaneous scaling transfor
mations in both the original Hamiltonian and the intertwining operator. It
is argued that in this way one can generate potentials with more interestin
g spectra than those obtained by means of the standard first-order intertwi
ning technique and, as an outcome, a simple engineering procedure is presen
ted. The harmonic oscillator potential is used in order to illustrate the p
revious statements, Moreover, a matrix representation of the scaled intertw
ining relationship is sketched up allowing for higher-dimensional generaliz
ations in the case of separable potentials.