We propose the Augmented Grouping Approach (AugGA) and its deployment in the Augmented Grouping GO (AugGGO) scheme, for an efficient exploration of the chemical ordering (or compositional structure) of multi-component (alloyed) nanoparticles. The approach is based on a 'grouping' strategy (previously proposed for high-symmetry structures) by which the number of compositional degrees of freedom of the system is decreased by defining sets of atoms (groups, or orbits, or shells) that are constrained to be populated by the same element. Three fundamental advances are here included with respect to previous proposals: (i) groups are defined on the basis of descriptors (no point-group symmetry is assumed), (ii) bulk groups can exploit general chemical ordering patterns taken from databases, and (iii) sub-grouping is realized via a multi-descriptor strategy (here using two basic descriptors: the atomic energy and a few types of geometry patterns). The AugGGO approach is applied to two prototypical examples of binary nanoalloys: Pd-Pt and Ag-Cu, with a size between ≈500 and ≈1300 atoms, in different configurations, and the convex hull of the mixing energy as a function of composition is derived. It is shown how the three advances here proposed decisively extend the power and scope of the grouping approach: (i) making it applicable to any generic structural framework, (ii) achieving a thorough sampling of the core regions of nanoparticles, and (iii) catching exotic/unexpected chemical ordering arrangements, at a computational cost which is 1-2 orders of magnitude smaller than that of traditional Monte Carlo single-exchange techniques.