Norovirus: This virus is a common cause of gastroenteritis, often presenting with diarrhea, nausea, vomiting, and sometimes upper respiratory symptoms like those of a URI. Its highly contagious nature and frequent outbreaks in closed environments (like cruise ships, schools, and hospitals) make it a leading consideration.

Rotavirus: Although vaccination has decreased its incidence, rotavirus can still cause severe gastroenteritis, especially in children, with symptoms including diarrhea, vomiting, and sometimes URI symptoms.
Adenovirus: Known for causing a wide range of infections, adenovirus can lead to gastroenteritis (with diarrhea and vomiting) and URI symptoms, making it a plausible diagnosis.
Astrovirus: This virus is another cause of gastroenteritis, particularly in children and the immunocompromised, presenting with diarrhea, vomiting, and occasionally URI symptoms.

Influenza: While primarily known for causing respiratory illness, certain strains of influenza can lead to gastrointestinal symptoms. Given the potential severity of influenza, especially in vulnerable populations, it's crucial not to miss this diagnosis.
COVID-19: The SARS-CoV-2 virus can cause a variety of symptoms, including those of a URI and gastrointestinal symptoms like nausea, vomiting, and diarrhea. The potential severity and the importance of public health measures make this a critical diagnosis not to overlook.

Sapovirus: A less common cause of gastroenteritis, sapovirus can lead to symptoms similar to norovirus, including diarrhea, vomiting, and occasionally URI symptoms.
Torovirus: Though rare, torovirus can cause gastrointestinal symptoms and has been associated with outbreaks of gastroenteritis, making it a consideration in the differential diagnosis, especially in specific epidemiological contexts.