We investigate multichromophoric energy transfer allowing for bath-induced fluctuations at different sites to be correlated. As a prototype system, we consider a light-harvesting antenna surrounding a reaction center. We show that the interplay between quantum coherence and correlated fluctuations can generate a room-temperature transfer process featuring a marked dependence on the degree of symmetry and delocalization of the initial exciton state. Our work illustrates how these quantum features could support fine-tuning of energy transfer efficiencies in closely packed natural and artificial light-harvesting complexes