Acute Fatty Liver of Pregnancy (AFLP): Given the patient's presentation with fever, thrombocytopenia (platelet count of 1.39 lakh), elevated liver enzymes (SGOT 7087, SGPT 364), and elevated bilirubin (1.5 with direct 1.4), AFLP is a strong consideration, especially in the context of the second trimester of pregnancy. The condition is characterized by acute liver failure in a previously healthy woman, often presenting with nonspecific symptoms such as nausea, vomiting, and abdominal pain, but can progress to more severe manifestations like coagulopathy and encephalopathy.

Hemolysis, Elevated Liver enzymes, and Low Platelet count (HELLP) Syndrome: Although the patient's platelet count is not as low as typically seen in HELLP syndrome, the combination of elevated liver enzymes and evidence of hemolysis (elevated LDH) makes this a plausible diagnosis. HELLP syndrome is a variant of preeclampsia and can present similarly to AFLP but often with more prominent hemolysis.
Viral Hepatitis: Despite the negative tests for common viral hepatitis (HAV, HEV, HCV, HBV), the possibility of a false-negative result or a less common viral hepatitis cannot be entirely ruled out. The clinical presentation could fit with an acute viral hepatitis, especially given the significant elevation in liver enzymes.

Preeclampsia with Severe Features: While the primary presentation does not include hypertension, preeclampsia can sometimes present atypically, especially in the context of severe organ dysfunction. The liver enzyme elevation and thrombocytopenia could be indicative of severe preeclampsia.
Disseminated Intravascular Coagulation (DIC): Given the thrombocytopenia and elevated liver enzymes, DIC should be considered, especially if there's any suspicion of an underlying condition that could precipitate it, such as a placental abruption or severe infection.

Wilson's Disease: An inherited disorder of copper metabolism that can present with acute liver failure, especially in young women. It's rare but should be considered in cases of unexplained liver disease.
Budd-Chiari Syndrome: A condition caused by thrombosis of the hepatic veins, leading to liver dysfunction. It's a rare cause of liver disease but could present with similar laboratory abnormalities.
Autoimmune Hepatitis: Although less common in pregnancy, autoimmune hepatitis could present with elevated liver enzymes and should be considered if other causes are ruled out.