It has been suggested that the Galactic cosmic rays may be accelerated by a two stage process in which one process, such as stellar flares, inject non-relativistic, super-thermal particles which are subsequently boosted to cosmic ray energies by some other mechanism, perhaps related to supernovae (eg. Cassé and Goret, 1978). Two-stage models in which the injection and re-acceleration processes are uncorrelated are apparently untenable because they cannot fit the observed energy dependence of the LiBeBN/CNO ratio. Here it is shown that additional contraints derived by considering the energy losses and nuclear reactions suffered by the super-thermal particles prior to their re-acceleration severely restrict other types of two-stage models.