As discussed in several places above, models of particular classes of collision have gotten quite sophisticated at this stage in the development of the field. However, in the case of specific systems this generalization is true only for systems that have experienced only one close encounter, or where the time between encounters is so long that the signatures of the first encounter have been largely erased. The one notable exception to this caveat is the M51 system, which may well be the result of two close encounters (see discussion in Struck(1999)).
There are wave and tidal morphologies characteristic of cases with two close passes separated by a time interval of order the mean internal dynamical (e.g., rotational) time in the primary disk. Struck-Marcell & Lotan(1990) demonstrated this explicitly in the case of colliding ring galaxies, and it is quite clear in a number of merger models. It also seems likely that a number of objects in the colliding galaxy atlases require two close encounters to explain their morphology (e.g., the M51 types).
Another kind of double encounter that has so far received only exploratory attention is the case when a galaxy falls into a group and has close encounters with more than one group member.
The study, and ultimately the classification, of double encounter morphologies and merger remnant systematics is one that could advance a long way in the next decade. There are no insurmountable technical difficulties preventing advancement, though a great deal of numerical effort will be required. Not only would a large number of simulations have to be run, but they would have to be fully self-consistent models. The ability to decipher two stages of development in colliding systems would represent a substantial advance in galaxy archaeology.