Motivated by recent observations and simulations of the formation of a cold and dense plasma sheet in the tail of the magnetosphere under northward interplanetary magnetic field (IMF) and of the direct influence of the plasma sheet density on the ring current strength, this paper aims at (1) highlighting how the coupling of these effects may lead to a preconditioning of the magnetosphere under northward IMF and (2) performing first tests of the validity of this hypothesis. We have analyzed superposed epoch time series of various parameters to investigate the response of the magnetosphere (as indicated by the Dst index) to the passage of coronal mass ejections (CMEs) and corotating interaction regions (CIRs). We first focused on the difference between the measured Dst signature and that predicted by a semiempirical Dst model. For both CME- and CIR-driven storms the superposed epoch results show that the model Dst predictions tend to underestimate the actual storm strength (by up to 10--30%) for events that are preceded by a substantial interval of northward IMF, as opposed to those with no such preceding northward IMF. We also analyzed Los Alamos geosynchronous spacecraft data for these events. The average density and temperature measured at storm onset are substantially higher and slightly lower, respectively, for the cases with preceding northward IMF intervals. These results suggest that solar wind structures may be more geoeffective if preceded by a northward IMF interval and they are consistent with the hypothesis of a preconditioning by a cold, dense plasma sheet. A colder and denser plasma sheet may lead to a stronger ring current when that plasma is convected inward during the main phase of an ensuing storm.