  A discussion of the overlap problem of reweighting approaches to evaluating
critical phenomenon in fermionic systems is motivated by highlighting the
divergence of the joint probability density function of a general ratio. By
identifying the bounds for which this integral can be expressed in closed form,
we establish criteria for accurately mapping the joint ratio distribution of
two disjoint ensembles through interpolation. The approach is applied to QCD
with four staggered flavours to evaluate the critical line in the $\beta-\mu$
plane.
