  Microlensing of extragalactic sources, in particular the probability of
significant amplifications, is a potentially powerful probe of the abundance of
compact objects outside the halo of the Milky Way. Accurate experimental
constraints require an equally accurate theoretical model for the amplification
statistics produced by such a population. In this article, we argue that the
simplest (strongest-lens) model does not meet this demanding requirement. We
thus propose an elaborate practical modelling scheme for extragalactic
microlensing. We derive from first principles an expression for the
amplification probability that consistently allows for: (i) the coupling
between microlenses; (ii) realistic perturbations from the cosmic large-scale
structure; (iii) extended-source corrections. An important conclusion is that
the external shear applied on the dominant microlens, both by the other lenses
and by the large-scale structure, is practically negligible. Yet, the
predictions of our approach can still differ by a factor of a few with respect
to existing models of the literature. Updated constraints on the abundance of
compact objects accounting for such discrepancies may be required.
