Multiple mating Narcissus flies?

I took some shots of Narcissus flies, Merodon equestris, mating this sunny morning on a dandelion flower. Initially there seemed to be two males, but one of them left. Editing them tonight I realised that the male that left had been mating to start with, and then the other male had mated with the female as well. The male mounting the female beated his wings continuously as if in flight, and the female used her long rear legs to half-heartedly swat at the male.
This is the sequence of shots showing both males mating in succession with the female.

The male behind the female is mating, the one on top beats its wings

The first male is dislodged

The second male mating (also in the top shot)

I have been unable to find - or access - published research about Merodon mating behaviour or how frequent this multiple mating is. It is also possible that I missed a struggle between the males and the second managed to dislodge the first one.  After mating, the female will look for daffodil or bluebell bulbs to oviposit. The larvae will feed on the bulbs and these will die or bear no flowers next spring.