It can happen but not like you may guess.
I believe you have seen rupture maps for large earthquakes, such as the 2011 Japan earthquake. In that earthquake, a foreshock of 7.3 took place at the perimeter of the area of largest slip during the main earthquake. This could be interpreted like this (using the asperity model): the foreshock hit at the "slopes" of the asperity but failed to "climb" up immediately; aftershocks were slowly migrating towards the "top" of the asperity, then the main shock happened. Furthermore, once the whole fault was activated, slip at the shallowest parts went beyond charts (40, 50, even 80m of slip were reported locally).
The main (deep) asperity had the fewest aftershocks (it slipped completely and without restraints), but there were enough of them in the shallowest parts of the fault. This is probably because the shallower slip was not due to an asperity but rather due to diffused slip of unconsolidated sediments (the "bookshelf" model was used, plus there were aftershocks that appeared to actually... pull back the pieces closer to their original locations). Anyways let's focus on the deeper asperity.
An earthquake can take place at the "slopes" of a large asperity but fail to rupture towards the "top" It can however rupture towards the perimeter and achieve respectable sizes. Then another earthquake can take place nearby, but still low at the "slopes". Finally an earthquake can climb over the top and force even the previously ruptured areas to re-rupture. All 3 earthquakes can very well have epicenters pretty close to one another (such as the two eastern Nepal aftershocks recently). It seems that the 1960 huge Valdivia earthquake demonstrated this behavior but I have yet to find a good, detailed, open-access study on it.
Concerning Fred's answer, unfortunately Bilham (he mentions Jones and Molnar, 1986) (search for "preceded") says that 10% of strong earthquakes in the history of Himalaya have been preceded by strong shocks. Other sources support Fred's answer, but I would choose to believe Bilham.
Concerning the "lots of aftershocks" notice that the author of the question pointed, for a given earthquake with a normal aftershock sequence it is expected that its strongest aftershock is 1.2 magnitude smaller than the mainshock. For this case, this would yield 6.6. In fact, the strongest ones were the 7.3, an 6.7 and a 6.6, so yes this is anomalous, but the empirical 1.2 value I mentioned is a bit smaller for Himalayas. Still, an 7.3 is anomalously large but before that time we had no reason to suspect an anomalous aftershock sequence (to my knowledge of course, I searched for b-values but did not find anything during the first days of aftershock activity).