Aminoglycosides (AGs) in combination with β-lactams play an important role in antimicrobial therapy in severe infections. Pan-resistance to clinically relevant AGs increasingly arises from the production of 16S rRNA methylases (RMTases) that are mostly encoded by plasmids in Gram-negative bacteria. The recent emergence and spread of isolates encoding RMTases is worrisome, considering that they often co-produce extended-spectrum β-lactamases (ESBLs) or carbapenemases. Our study aimed to retrospectively analyze and characterize the association of carbapenem- and aminoglycoside-resistant clinical isolates in Switzerland during a 3.5-year period between January 2017 and June 2020. A total of 103 pan-aminoglycoside- and carbapenem-resistant clinical isolates were recovered at the NARA (Swiss National Reference Center for Emerging Antibiotic Resistance) during the 2017-2020 period. Carbapenemase and RMTase determinants were identified by PCR and sequencing. The characterization of plasmids bearing resistance determinants was performed by a mating-out assay followed by PCR-based replicon typing (PBRT). Clonality of the isolates was investigated by multilocus sequence typing (MLST). Over the 991 Enterobacterales collected at the NARA during this period, 103 (10.4%) of them were resistant to both carbapenems and all aminoglycosides. Among these 103 isolates, 35 isolates produced NDM-like carbapenemases, followed by OXA-48-like (n = 23), KPC-like (n = 21), or no carbapenemase (n = 13), OXA-48-like and NDM-like co-production (n = 7), and VIM-like enzymes (n = 4). The RMTases ArmA, RmtB, RmtC, RmtF, RmtG, and RmtB + RmtF were identified among 51.4%, 13.6%, 4.9%, 24.3%, 1%, and 1%, respectively. Plasmid co-localization of the carbapenemase and the RMTase encoding genes was found among ca. 20% of the isolates. A high diversity was identified in terms of the nature of associations between RMTase and carbapenemase-encoding genes, of incompatibility groups of the corresponding plasmids, and of strain genetic backgrounds, highlighting heterogeneous importations rather than clonal dissemination.