The prediction of self-excited combustion instabilities in a can-annular gas turbine combustion system is a significant challenge, mainly because the instabilities originate from the acoustic interactions between adjacent combustors via a cross-talk region upstream of the first stage turbine nozzles. Detailed characterization of these instabilities requires a thorough understanding of engine-level dynamics. Until now, a comprehensive experimental examination of such a can-annular configuration had not been conducted. Here we present new experiments using four lean fully-premixed swirl-stabilized combustors connected via a full-annular cross-talk section. We demonstrate that the global fluctuations at limit cycles are either in-phase interactions (push-push modes) or one of two different forms of out-of-phase interactions (push-pull modes), subject to uniform and non-uniform equivalence ratio combinations. Under certain symmetric conditions, the can-annular system undergoes in-phase synchronous modulations (Type I), giving rise to the formation of pressure antinodes at the inlets of the four combustors and in the cross-talk region. By contrast, out-of-phase interactions are sustained in the form of either an alternating pattern in four-coupled combustors (Type II) or a push-pull interaction in two opposite combustors only (Type III). The latter is dictated by strong out-of-phase fluctuations between two of the combustors and a pressure node-like condition - thermoacoustically decoupled from the global fluctuations - over the entire region of the other two combustors, experimentally demonstrating the existence of mode localization in can-annular thermoacoustic instabilities. We show that the mode clustering phenomenon is responsible for the excitation of closely-spaced multiple eigenmodes in the can-annular acoustic environment, and as a consequence the system can feature a mixed state with several distinct types of interaction patterns. By analyzing a large amount of experimental data acquired systematically for coupled two-combustor and four-can-annular configurations, we demonstrate that longitudinal-mode instabilities in a can-annular combustion system will preferentially emerge in the form of out-of-phase interactions.