In this contribution, by using the most characteristic seminal Arlequin method idea, namely the volume/thick-models/scales coupling, relying on a superposition of subdomains pillar (see [1], [2]), we extend the Non-Intrusive-Global-Local Iterative (NIGLI) method, developed by Allix, Gosselet and their collaborators (see e.g. [3, 4]) ; an advanced, more robust and practically more interesting version of the Whitcomb’s Iterative Global-Local method (see [5]), to solve true-complex problems requiring, for costs sustainability, the coupling of global coarse models and localized non-local-ones i.e. true-multiscale problems that can not be solved by the NIGLI method.