In the context of time harmonic wave scattering by piecewise homogeneous penetrable objects, we present a new variant of the multi-trace boundary integral formulation, that differs from the local multi-trace approach of [Jerez-Hanckes \& Hiptmair, 2012], by the presence of regularisation terms involving boundary integral operators and localised at junctions i.e. points where at least three subdomains abut. We prove well-posedness and quasi-optimal convergence of conforming Galerkin discretisations for this new formulation, and present numerical results.