We extended the procedure of pseudo Jahn-Teller effect (PJTE) analysis of the origin of instability of molecular high-symmetry configuration to relatively large organic compounds containing several ring-structures by exploring two types of possible distortions: the buckyball non-planarity of sumanenes and its derivatives, and the torsional rotations in two-ring and four-ring thiophenes. We performed electronic structure calculations of the ground and several excited states of these systems and revealed their main excited states that contribute to their instability in the ground state as well as the numerical values of the parameters of the PJTE. The findings describe in detail the interim mechanism that controls the main structural properties of these compounds, opening the possibility to manipulate them by targeting the PJTE features that are vulnerable to external influence. Among other details, the analysis of the PJTE shows how tri-atomic substitutions in sumanenes influence their buckling instability, especially the intriguing origin of the difference between tri-oxygen and tri-sulfur substitutions, the former being much stronger than the latter. The worked out procedures of application of the PJTE theory to such relatively large organic compounds can be used for studies of other systems and other kind of distortions.