Chronic Myeloid Leukemia (CML): This condition is characterized by an overproduction of mature and immature granulocytes, which could explain the high WBC count with a predominance of neutrophils. The elevated MCV (mean corpuscular volume) might indicate a reactive response or a secondary effect of the leukemia on red blood cell production, and the low red blood cell count could be due to bone marrow replacement by leukemic cells.

Infection: A severe bacterial infection can cause a significant increase in WBC count, particularly neutrophils, as part of the body's immune response. The infection could also lead to anemia of chronic disease, explaining the low red blood cell count.
Chronic Inflammation: Conditions like rheumatoid arthritis or other autoimmune diseases can cause chronic inflammation, leading to an elevated WBC count, including neutrophils, and potentially affecting red blood cell production.
Myeloproliferative Neoplasms (MPN): Other than CML, conditions like Polycythemia Vera (PV), Essential Thrombocythemia (ET), and Primary Myelofibrosis (PMF) can present with elevated WBC counts and alterations in other blood cell lines, though the specific pattern can vary.

Sepsis: Although it might seem like an obvious diagnosis, sepsis can present subtly and is critical not to miss due to its high mortality rate. The body's response to severe infection can include a high WBC count with a left shift (indicating immature neutrophils), low red blood cell count due to inflammation, and potentially altered MCV.
Acute Myeloid Leukemia (AML): AML is a medical emergency that can present with similar laboratory findings to CML but often with more severe symptoms and a higher risk of rapid deterioration. It's crucial to distinguish AML from CML due to differences in treatment and prognosis.

Myelodysplastic Syndromes (MDS): These are a group of disorders caused by poorly formed or dysfunctional blood cells, which can lead to various cytopenias (low blood cell counts) and sometimes an increase in certain cell lines. While MDS can present with a high WBC count, it's less common and usually accompanied by other specific findings.
Paroxysmal Nocturnal Hemoglobinuria (PNH): A rare, acquired, life-threatening disease of the blood characterized by the destruction of red blood cells, bone marrow failure, and the potential for blood clot formation. It might present with anemia, variable white blood cell counts, and sometimes an elevated MCV due to reticulocytosis (increase in immature red blood cells).