A methodological approach based on reverse transcription (RT)-multiplex PCR followed by next-generation sequencing (NGS) was implemented to identify multiple respiratory RNA viruses simultaneously. A convenience sampling from respiratory surveillance and SARS-CoV-2 diagnosis in 2020 and 2021 in Montevideo, Uruguay, was analyzed. The results revealed the cocirculation of SARS-CoV-2 with human rhinovirus (hRV) A, B and C, human respiratory syncytial virus (hRSV) B, influenza A virus, and metapneumovirus B1. SARS-CoV-2 coinfections with hRV or hRSV B and influenza A virus coinfections with hRV C were identified in adults and/or children. This methodology combines the benefits of multiplex genomic amplification with the sensitivity and information provided by NGS. An advantage is that additional viral targets can be incorporated, making it a helpful tool to investigate the cocirculation and coinfections of respiratory viruses in pandemic and post-pandemic contexts.