Can-to-can acoustic interactions in a circumferential network of lean-premixed combustors have a prominent role in the development of complicated modal dynamics and large-scale pattern formations in can-annular gas turbine combustion systems. Despite recent progress in understanding these instabilities, however, previous relevant studies have been limited to an even number of constituent combustors; a fundamental characteristic of the modal dynamics in a can-annular arrangement consisting of an odd number of combustors remains unknown. To address this question, we compare key features of thermoacoustic instabilities in four-coupled (N = 4) and five-coupled (N = 5) can-annular combustor configurations obtained over a broad range of operating conditions. In conjunction with FEM-based Helmholtz simulations, our experimental data show that the dynamic behavior of the even-N case is characterized by the well-known interaction pattern, out-of-phase alternating modulations among the networked combustors. For the odd-N case, however, the can-annular system features complex phase dynamics originating from simultaneous excitation of the degenerate mode pair. We highlight that the development of self-excited azimuthal instabilities in the annular cross-talk section is associated with the modal interaction of the degenerate pair in the odd-N configuration. The initially degenerate pair can be split into two closely-spaced non-degenerate modes, and in consequence their modal interaction gives rise to a periodic transition between spinning and standing azimuthal modes in the annulus. Despite the formation of remarkably different inter-combustor interactions in the two can-annular configurations, however, the entire set of instability data collapses into very similar frequency regimes, suggesting the importance of flame-acoustic interactions occurring within each combustor, namely intra-combustor interactions.