  Given a family of varieties over the projective line, we study the density of
fibres that are everywhere locally soluble in the case that components of
higher multiplicity are allowed. We use log geometry to formulate a new
sparsity criterion for the existence of everywhere locally soluble fibres and
formulate new conjectures that generalise previous work of Loughran-Smeets.
These conjectures involve geometric invariants of the associated multiplicity
orbifolds on the base of the fibration in the spirit of Campana. We give
evidence for the conjectures using Chebotarev's theorem and sieve methods.
