Polycythemia Vera: This condition is characterized by an overproduction of red blood cells, white blood cells, and platelets. High iron levels can contribute to the increased production of hemoglobin, leading to elevated hemoglobin levels. The low MCV (mean corpuscular volume) and MCHC (mean corpuscular hemoglobin concentration) can be seen due to the variability in red blood cell size and hemoglobin content, although typically, polycythemia vera might present with a normal or slightly elevated MCV. However, the combination of high iron and high hemoglobin with other clinical features such as thrombocytosis and leukocytosis would point towards this diagnosis.

Chronic Dehydration: Dehydration can cause a relative increase in hemoglobin concentration due to decreased plasma volume, leading to high hemoglobin levels. If the dehydration is chronic, it might also affect iron levels and red blood cell indices, potentially resulting in low MCV and MCHC due to changes in red blood cell production and survival.
Androgen Use: The use of androgenic steroids can increase red blood cell production, leading to elevated hemoglobin levels. This condition might also present with low MCV and MCHC, especially if there's an imbalance in erythropoiesis or if the patient has underlying iron metabolism alterations.

Erythrocytosis due to Hypoxia: Conditions that lead to chronic hypoxia (e.g., chronic obstructive pulmonary disease, sleep apnea) can stimulate erythropoietin production, increasing red blood cell production and hemoglobin levels. Although MCV and MCHC might not be directly affected, missing this diagnosis could lead to untreated underlying conditions causing hypoxia.
Renal Cell Carcinoma: Some renal cell carcinomas can produce erythropoietin, leading to secondary erythrocytosis. This condition is crucial not to miss due to its potential for severe outcomes if left untreated.

Congenital Erythrocytosis: This is a rare condition characterized by an increase in red blood cell mass due to genetic mutations affecting the erythropoietin receptor or other pathways involved in erythropoiesis. It might present with high hemoglobin and alterations in MCV and MCHC, depending on the specific mutation and its effect on red blood cell production.
High-Altitude Adaptation: Individuals living at high altitudes may develop increased red blood cell production as an adaptation to lower oxygen levels, potentially leading to elevated hemoglobin levels. The effect on MCV and MCHC can vary, but this condition is worth considering in individuals with recent exposure to high altitudes.