Pion-induced pion production on the deuteron was studied via the reactions +d-+pp and -d+-nn. The doubly differential cross sections for these reactions were measured, covering the center-of-mass phase space at incident pion energies of 256, 331, and 450 MeV. Calculations of the quasifree production process on one nucleon were performed in a plane-wave approximation using a phenomenological, on-shell -p+-n amplitude. Comparison of the data with the calculations indicates that the quasifree mechanism dominates these production reactions on the deuteron. Upper limits for bound -nn and +pp systems with small binding energies were also measured. The possible existence of a resonance in these systems near the production threshold was investigated.