Nothing was mentioned about a second or third major earthquake happening shortly after a major earthquake; even for the devastating 1934 earthquake.

Due to the different tectonic settings and causes for earthquakes in different parts of the world it is best not to look at the history of one part of the world and assume the same will occur elsewhere. The expectancy of earthquakes and their patterns in the Himalayas should not be compared with earthquakes in Japan, New Zealand, western USA, Turkey or elsewhere.

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).