Metastatic Squamous Cell Carcinoma: Given the presence of a hypermetabolic left parotid mass, a right upper lobe (RUL) mass, marked mediastinal hypermetabolic nodes, a right lobe hepatic mass, and matted hypermetabolic nodes in the region of the pancreatic head and body, the most likely diagnosis is a metastatic squamous cell carcinoma, potentially originating from the head and neck region (given the parotid mass) and metastasizing to the lung, liver, and lymph nodes.

Lymphoma: The widespread involvement of lymph nodes, including those in the mediastinum and around the pancreatic head and body, along with masses in the parotid, lung, and liver, could also suggest lymphoma, particularly if the patient has systemic symptoms.
Metastatic Lung Cancer: A primary lung cancer (given the RUL mass) with metastases to the parotid gland, liver, and lymph nodes is another possibility, especially if the lung mass is large and the parotid mass is considered a metastasis.

Infectious or Inflammatory Processes: Although less likely given the pattern of hypermetabolic activity, infectious (e.g., tuberculosis, fungal infections) or inflammatory processes (e.g., sarcoidosis) could mimic metastatic disease and would have significantly different management, making them crucial not to miss.
Lymphoproliferative Disorders: Disorders like Castleman disease could present with similar lymph node involvement and should be considered, especially if lymphoma is a concern.

Metastatic Salivary Gland Tumors: While the parotid mass could be a primary salivary gland tumor, metastatic disease from other sites (e.g., breast, melanoma) to the parotid gland, lung, liver, and lymph nodes is rare but possible.
Neuroendocrine Tumors: Although less common, neuroendocrine tumors (e.g., pancreatic neuroendocrine tumors) could present with metastases to the liver, lymph nodes, and other sites, and might show hypermetabolic activity on PET scans.