(1) Background: The rise of multi-antibiotic resistant bacteria represents an emergent threat to human health. Here, we investigate antibiotic resistance mechanisms in bacteria of several species isolated from an intensive care unit in Brazil. (2) Methods: We used whole-genome analysis to identify antibiotic resistance genes (ARGs) and plasmids in 34 strains of Gram-negative and Gram-positive bacteria, providing the first genomic description of Morganella morganii and Ralstonia mannitolilytica clinical isolates from South America. (3) Results: We identified a high abundance of beta-lactamase genes in resistant organisms, including seven extended-spectrum beta-lactamases (OXA-1, OXA-10, CTX-M-1, KPC, TEM, HYDRO, BLP) shared between organisms from different species. Additionally, we identified several ARG-carrying plasmids indicating the potential for a fast transmission of resistance mechanism between bacterial strains. Furthermore, we uncovered two pairs of (near) identical plasmids exhibiting multi-drug resistance. Finally, since many highly resistant strains carry several different ARGs, we used functional genomics to investigate which of them were indeed functional. In this sense, for three bacterial strains (Escherichia coli, Klebsiella pneumoniae, and M. morganii), we identified six beta-lactamase genes out of 15 predicted in silico as those mainly responsible for the resistance mechanisms observed, corroborating the existence of redundant resistance mechanisms in these organisms. (4) Conclusions: Systematic studies similar to the one presented here should help to prevent outbreaks of novel multidrug-resistant bacteria in healthcare facilities.