A new view on how large disturbances in the magnetosphere may be prolonged and intensified further emerges from a recently discovered interplanetary process: the collision/merger of interplanetary (IP) coronal mass ejections (ICMEs; ejecta) within 1 AU. As shown in a recent pilot study, the merging process changes IP parameters dramatically with respect to values in isolated ejecta. The resulting geoeffects of the coalesced ("complex") ejecta reflect a superposition of IP triggers which may result in, for example, two-step, major geomagnetic storms. In a case study, we isolate the effects on ring current enhancement when two coalescing ejecta reached Earth on 31 March 2001. The magnetosphere "senses" the presence of the two ejecta and responds with a reactivation of the ring current soon after it started to recover from the passage of the first ejection, giving rise to a double-dip (DD) great storm (each min Dst < -250 nT). A drift-loss global kinetic model of ring current buildup shows that in this case the major factor determining the intensity of the storm activity is the very high (up to ~10 cm-3) plasma sheet density. The plasma sheet density, in turn, is found to correlate well with the very high solar wind density, suggesting the compression of the leading ejecta as the source of the hot, superdense plasma sheet in this case. This correlation is similar to that obtained in a previous investigation extending over several years, but the present case study extends the range of plasma sheet densities from ~2 to ~10 cm-3. Since the features of the ejecta interaction in this example are fairly general, we propose that interacting ejecta are a new, important IP source of DD major storms. Peculiarities in the behavior of the magnetopause current during these extreme events are briefly discussed in the light of recent work. In a brief discussion of a second example (21--23 October 2001), we suggest that by strengthening the leading shock, the ejecta merger may have added to the "shock-driver gas" origin of DD geomagnetic storms by increasing the ability of the shock to compress preexisting Bz < 0 magnetic fields.