Since the reconstruction of an event is time-consuming (to put it mildly), one wants to put more than one embedded pair into an event. On the other hand, the embedded pairs should not strongly change the nature of the "mother" event. Furthermore, if we want to understand things pair-wise, we should keep the pairs from interfering with each other.
Here is a (low-resolution) picture of 6 pairs put into a Au+Au collision at 2 GeV. The relative momentum for all pairs is 50 MeV/c, and the average momentum of the pairs in z is 500 MeV/c and Pt = 300 MeV/c. The azimuthal angle of the pairs differs so that they do not interfere strongly with one another (see right hand panel).
Although the .gif file is too low resolution to see them by eye, the tracker does resolve all of the pairs embedded in this event.