Polycythemia Vera: This is a myeloproliferative disorder characterized by the overproduction of red blood cells, white blood cells, and platelets. Elevated hemoglobin (Hgb) is a hallmark, and elevated bilirubin can occur due to increased red blood cell turnover. The combination of these two findings, along with other clinical features such as thrombocytosis and leukocytosis, makes polycythemia vera a leading consideration.

Hemolytic Anemias: Conditions like hereditary spherocytosis, autoimmune hemolytic anemia, or glucose-6-phosphate dehydrogenase (G6PD) deficiency can lead to elevated bilirubin due to hemolysis. While these conditions typically present with anemia, some cases might have a compensatory increase in erythropoiesis, potentially leading to elevated or normal Hgb levels initially.
Chronic Liver Disease: Liver diseases such as cirrhosis can cause an increase in bilirubin levels. Although liver disease is more commonly associated with anemia, some patients might have a relative polycythemia due to factors like diuretic use leading to hemoconcentration.
Dehydration: Dehydration can cause a relative increase in Hgb concentration due to hemoconcentration and can also lead to elevated bilirubin levels if there is associated liver dysfunction or hemolysis.

Sickle Cell Disease with Splenic Sequestration: Although typically associated with anemia, sickle cell disease can have periods of elevated Hgb during episodes of splenic sequestration, where red blood cells are trapped in the spleen, potentially leading to a temporary increase in circulating Hgb. Elevated bilirubin is common due to chronic hemolysis.
Hemoglobinopathies with Co-existing Conditions: Certain hemoglobinopathies like beta-thalassemia major can have elevated Hgb levels when co-existing with conditions that cause erythrocytosis, and bilirubin can be elevated due to hemolysis.
Paroxysmal Nocturnal Hemoglobinuria (PNH): A rare, acquired, life-threatening disease of the blood characterized by the destruction of red blood cells (hemolysis), bone marrow failure, and the potential for blood clot formation (thrombosis). It can present with elevated bilirubin due to hemolysis and potentially elevated Hgb in certain phases.

Erythrocytosis due to Testosterone Replacement Therapy: Exogenous testosterone can stimulate erythropoiesis, leading to elevated Hgb levels. If there's associated hemolysis or liver dysfunction, bilirubin could also be elevated.
High-Altitude Erythrocytosis: Living at high altitudes can lead to an increase in red blood cell production (erythrocytosis) as an adaptation to lower oxygen levels. This could potentially be associated with elevated bilirubin if there's increased red blood cell turnover.
Familial Erythrocytosis: Rare genetic conditions that lead to increased erythropoietin production or sensitivity, resulting in elevated Hgb levels. Associated conditions could lead to elevated bilirubin.