We report three-dimensional structures--mesoscale "atoms"--comprising up to N=8 aqueous droplets compressed in a liquid shell. In contrast to hard colloids that self-assemble into structures unique for a given N, we observe multiple metastable states. We attribute this unexpected richness of metastable structures to the deformability of the cores that introduces irreducible many-body interactions between the droplets. These exotic, often highly anisotropic, structures are locally stable. The structures displaying highly nonoptimum packing-and hence interfacial energy much higher than that of the lowest-energy state-exhibit finite energy barriers that prevent restructuring and relaxation of energy.