The inadequacy of standard few-body approaches in describing the πNN system has motivated searches for the responsible missing mechanism. In the case of πd scattering, it has recently been asserted that an additional short range ΔN interaction can account for essentially all the discrepancies between a few-body calculation and experimental data. This conclusion, however, has been based on calculations where a phenomenological ΔN interaction is added only in Born term to background few-body amplitudes. In the present work we investigate the effect of including such a ΔN interaction to all orders within a unitary few-body calculation of the NN system. Besides testing the validity of adding the ΔN interaction in Born term in d scattering, our fully coupled approach also enables us to see the influence of the same ΔN interaction on the processes NN→πd and NN→NN. For πd elastic scattering, we find that the higher order ΔN interaction terms can have as much influence on πd observables as the lowest order contribution alone. Moreover, we find that the higher order contributions tend to cancel the effect obtained by adding the ΔN interaction in Born term only. The effect of the same ΔN interaction on NN→πd and NN→NN appears to be as significant as in πd→πd, suggesting that future investigations of the short range ΔN interaction should be done in the context of the fully coupled πNN system.