Reactive Arthritis: This condition is characterized by the development of arthritis following a gastrointestinal or genitourinary infection. The migratory, non-erosive, and asymmetrical nature of the polyarthritis, combined with hepatitis, could be indicative of a reactive process, especially if triggered by a bacterial infection such as Salmonella, Shigella, or Yersinia, which can also cause hepatitis.

Rheumatoid Arthritis (RA): Although RA typically presents with symmetrical arthritis, early stages can be asymmetrical. Hepatitis can be a manifestation of RA itself or a side effect of medications used to treat RA. However, the migratory pattern is less common in RA.
Psoriatic Arthritis (PsA): PsA can present with asymmetrical, non-erosive arthritis and is associated with psoriasis. Hepatitis could be related to the disease itself or to medications. The migratory pattern can be seen in PsA, especially in the context of the "arthritis mutilans" subtype, though this is less common.
Lyme Disease: Caused by Borrelia burgdorferi, Lyme disease can present with migratory arthritis and, in rare cases, hepatitis. The pattern of arthritis and the presence of hepatitis, especially in endemic areas, make this a consideration.

Gonococcal Arthritis: This is a serious condition caused by Neisseria gonorrhoeae that can present with migratory arthritis, dermatitis, and tenosynovitis. Hepatitis can occur due to disseminated gonococcal infection. It's crucial to consider this diagnosis due to its potential for severe consequences if untreated, including sepsis and long-term joint damage.
Endocarditis: Infective endocarditis can cause arthritis and hepatitis as part of its systemic manifestations. The diagnosis is critical due to the high mortality rate if left untreated.
Sarcoidosis: Although less common, sarcoidosis can cause arthritis and hepatitis. It's a diagnosis that should not be missed due to its potential for significant morbidity if not properly managed.

Whipple's Disease: A rare, systemic bacterial infection (Tropheryma whipplei) that can cause migratory arthritis, hepatitis, and other systemic symptoms. Diagnosis is challenging and requires a high index of suspicion.
Brucellosis: A zoonotic infection that can cause arthritis, hepatitis, and other systemic symptoms. It's rare in many parts of the world but should be considered in individuals with exposure to infected animals or their products.
Parvovirus B19 Infection: Can cause arthritis and, less commonly, hepatitis. It's more commonly associated with the fifth disease in children but can cause significant morbidity in adults, especially those with underlying conditions.