This retrospective study analysed the routine data obtained by multiplex real-time RT-qPCR methods for respiratory virus detection. A total of 4814 respiratory specimens collected during 1 September 2022–31 August 2023 were included in the study. A total of 38% of the specimens were positive for at least one target, with the incidence maximum (82%) for the small children (age group 0–4 years). The five dominant virus groups were rhinovirus (RV, 12%), influenza virus A (IAV, 7%), adenovirus (AdV, 6%), respiratory syncytial virus (RSV, 5%), and severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, 5%). The specimens with multi-detections represented 19% of the positives, unevenly distributed (n = 225, 56, 43, 24) among the age groups 0–4, 5–14, 15–64, and 65< years, respectively. The dominant virus groups in multi-positive specimens were RV (53%), AdV (43%), and bocavirus (BoV, 35%)—in mutual pairs as well as all three together—followed by RSV (21%), and IAV (15%). Our study focused on the specimens with codetections and provides an insight into the variety of the respiratory virus interactions in Latvia during the first year since pandemic-related social restriction measures were eased. The observations also emphasise the need to consider the differentiation between rhinoviruses and enteroviruses, especially for the youngest patients in the age group 0–4.