Tuberculosis (TB): Given the combination of prolonged fevers, low back pain (which could indicate spinal involvement), and hepatomegaly, TB is a strong consideration. TB can affect multiple systems, including the skeletal, hepatic, and lymphatic systems, making it a unifying diagnosis for these symptoms.

Pyogenic Liver Abscess: This condition can cause fever, hepatomegaly, and potentially low back pain if the abscess is large enough to cause referred pain or if there is associated psoas abscess.
Endocarditis: Infective endocarditis can present with fever, and embolic phenomena can cause low back pain (e.g., spinal cord infarction or vertebral body infection). Hepatomegaly can occur due to septic emboli or congestive heart failure.
Lymphoma: Both Hodgkin's and non-Hodgkin's lymphoma can present with systemic symptoms like fever, hepatomegaly due to liver involvement, and low back pain from vertebral body involvement.

Spinal Epidural Abscess: Although less common, this is a medical emergency that requires prompt diagnosis and treatment. It can cause fever, severe back pain, and neurological deficits. The presence of hepatomegaly might be incidental or related to another process, but the combination of fever and back pain mandates consideration of this diagnosis.
Osteomyelitis: Particularly if the low back pain is severe and localized, osteomyelitis of the spine (vertebral osteomyelitis) should be considered. It can cause fever and, if the infection spreads, potentially hepatomegaly due to systemic infection or abscess formation.
Psoas Abscess: A psoas abscess can cause severe low back pain and fever. While hepatomegaly might not be directly related, it could be part of a systemic response to infection.

Whipple's Disease: A rare, systemic bacterial infection that can cause fever, weight loss, diarrhea, joint pain, and hepatomegaly. Low back pain could be due to associated conditions like osteoporosis or less commonly, direct spinal involvement.
Brucellosis: A zoonotic infection that can cause fever, hepatomegaly, and musculoskeletal symptoms including back pain. It's rare in many areas but should be considered in individuals with exposure to livestock or unpasteurized dairy products.
Familial Mediterranean Fever: An autosomal recessive disorder characterized by recurrent episodes of fever, often accompanied by severe abdominal, chest, or joint pain. Hepatomegaly can occur, and while back pain is less common, it could be part of the symptom complex in some cases.