Viral gastroenteritis: This diagnosis is the most likely due to the combination of symptoms such as pharyngitis, cough, anorexia, and diarrhea, which are commonly seen in viral infections affecting the gastrointestinal and respiratory systems.

Influenza: Given the symptoms of pharyngitis, cough, and anorexia, influenza is a plausible diagnosis, especially during flu season. The presence of diarrhea, although less common, can occur in some cases.
Respiratory syncytial virus (RSV) infection: RSV can cause a range of symptoms from mild upper respiratory tract infections to severe lower respiratory tract infections, and it might be considered, especially in pediatric patients or during RSV season.
Adenovirus infection: Adenoviruses can cause a variety of clinical syndromes, including pharyngitis, cough, and gastrointestinal symptoms like diarrhea, making it another possible diagnosis.

Pertussis (Whooping Cough): Although less common due to vaccination, pertussis can present with cough and might be accompanied by other symptoms like pharyngitis and anorexia. It's crucial to consider this diagnosis due to its potential for severe complications, especially in infants and those not vaccinated.
Infectious mononucleosis: Caused by Epstein-Barr virus (EBV), this condition can present with pharyngitis, fever, and anorexia. While diarrhea is not a primary symptom, it could be a secondary effect due to the illness's impact on the body.
Streptococcal pharyngitis: Although primarily known for causing throat infections, streptococcal infections can occasionally be associated with gastrointestinal symptoms. It's essential to consider this diagnosis due to the potential for complications like rheumatic fever if left untreated.

Cytomegalovirus (CMV) infection: CMV can cause a wide range of symptoms, including pharyngitis, diarrhea, and systemic illness, particularly in immunocompromised individuals.
Myocarditis or pericarditis: These conditions, often caused by viral infections, can present with systemic symptoms like anorexia and might be accompanied by respiratory or gastrointestinal symptoms, although they are less directly related to the primary symptoms described.