Abstract Thermoacoustic interactions in a circumferential network of lean-premixed combustors have a substantial impact on engine-level dynamics in a can-annular gas turbine combustion system. Previous experimental and numerical studies have focused on identifying the formation of large-scale interaction patterns and the modal dynamics of multiple eigenmodes. Since those investigations were primarily concerned with low-frequency interactions between adjacent combustors, there are currently no experimental observations that enable decisive discrimination between low- and high-frequency can-annular combustion instabilities. Here, we use pure hydrogen-air flame ensembles to trigger higher acoustic modes in four-coupled lean-premixed combustors, ultimately to understand the potential influence of self-excited instabilities on the spatiotemporal evolution of a can-annular system. The use of lean-premixed hydrogen-air flames enables measurements of previously unidentified phenomena, particularly in association with the excitation of high acoustic modes up to approximately 1.3 kHz. We demonstrate that self-excited standing azimuthal modes can be excited in the annular cross-talk section, particularly when the phase dynamics of the upstream flame tube sections are defined by alternating anti-phase oscillations. In this case, the temporal evolution of the can-annular system is governed by twofold degeneracy, incorporating an alternating push-pull mode in the longitudinal direction and a standing azimuthal mode in the circumferential direction at the same frequency. Based on experimental observations and Helmholtz simulations, we also show that a mixed state of synchronization and desynchronization can arise simultaneously as a result of symmetry breaking. The coexistence of coherent and incoherent motions is observed to be controlled by interactions between two closely spaced, but slightly misaligned, localized in-phase modes; this observation demonstrates experimentally the existence of a chiral state in can-annular thermoacoustics. The present results, for the first time, reveal a variety of phenomena involved in the response of a can-annular combustion system to higher frequency acoustic perturbations.