Dehydration: This condition can cause a relative increase in RBC count due to decreased plasma volume, and low MCH (mean corpuscular hemoglobin) can be seen due to the body's attempt to maintain oxygen delivery despite the decreased plasma volume.

Chronic Hypoxia: Conditions leading to chronic hypoxia, such as chronic obstructive pulmonary disease (COPD) or living at high altitudes, can stimulate erythropoiesis, leading to an increased RBC count. The low MCH might be due to inadequate iron supply or utilization in the face of increased erythropoietic demand.
Polycythemia Vera: A myeloproliferative disorder that can cause an increase in all three blood cell lines, including RBCs. Low MCH might be seen due to the disorder's effect on erythropoiesis, potentially leading to the production of smaller, less hemoglobin-rich red cells.

Severe Iron Deficiency Anemia: Although it might seem counterintuitive, severe iron deficiency can lead to a high RBC count as the body attempts to compensate for the lack of hemoglobin by producing more red cells, albeit smaller and less hemoglobin-rich ones (low MCH). Missing this diagnosis could lead to untreated anemia and its complications.
Chronic Blood Loss: Similar to iron deficiency anemia, chronic blood loss can lead to increased erythropoiesis, resulting in a high RBC count with low MCH due to the rapid production of red cells without adequate hemoglobinization.

Erythrocytosis due to EPO Abuse or Exogenous EPO Administration: This can cause an increase in RBC production, potentially leading to high RBC counts. Low MCH might be observed if there's an imbalance in the production of red cells versus the availability of hemoglobin.
Myelodysplastic Syndromes (MDS): Certain types of MDS can lead to ineffective erythropoiesis, resulting in a high RBC count with morphological abnormalities, including low MCH. These syndromes are rare and require careful diagnosis to distinguish from other causes of anemia and cytopenias.