Viral Infection: Many viral infections can cause an increase in white blood cell (WBC) count due to a rise in lymphocytes, while simultaneously causing a relative or absolute decrease in neutrophils. This is a common and likely scenario in clinical practice.

Bacterial Infection with Neutropenia: Certain bacterial infections can lead to an increased WBC count as the body responds to the infection, but if the infection is severe, it can also consume neutrophils, leading to a low neutrophil count.
Chronic Leukemia: Leukemias, especially chronic lymphocytic leukemia (CLL), can present with an elevated WBC count due to the proliferation of lymphocytes, and may also lead to a decrease in the production or function of neutrophils.
Severe Bone Marrow Suppression: Conditions or treatments that severely suppress the bone marrow can lead to an increase in certain WBC lines (like lymphocytes) while decreasing others (like neutrophils), due to the differential effects on various cell lines.

Aplastic Anemia: Although rare, aplastic anemia is a condition where the bone marrow fails to produce blood cells, including neutrophils. It can present with a low neutrophil count and may have a variable WBC count, but it's crucial to diagnose early due to its severe implications.
Sepsis with Neutropenia: Sepsis, especially when caused by certain bacteria, can lead to both an elevated WBC count and a low neutrophil count. Missing this diagnosis can be fatal.
HIV/AIDS: Infection with HIV can lead to a variety of hematologic abnormalities, including an elevated WBC count with a low neutrophil count. Early diagnosis is critical for management and prognosis.

Myelodysplastic Syndromes (MDS): These are a group of disorders caused by poorly formed or dysfunctional blood cells, which can lead to an elevated WBC count with a specific lineage affected (like neutropenia) due to the bone marrow's ineffective production.
Lymphoma: Certain types of lymphoma can present with an elevated WBC count and a low neutrophil count, especially if there is significant bone marrow involvement.
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 can present with variable hematologic findings, including an elevated WBC count and low neutrophil count.