Bone metastasis or primary bone malignancy: Elevated alkaline phosphatase (ALP) can indicate bone involvement, and an elevated white blood cell (WBC) count can be seen in response to malignancy or infection. This combination is commonly seen in patients with bone metastases or primary bone cancers.

Infection: An elevated WBC count is a common response to infection. While ALP can be elevated in some infections (like osteomyelitis), this combination could also represent a concurrent bone or liver condition alongside an infection.
Liver disease: Elevated ALP can be seen in various liver diseases, including cholestasis. A mildly elevated WBC count could be a non-specific response to illness or could indicate an infectious component.
Paget's disease of bone: This condition can cause elevated ALP due to increased bone turnover. A mildly elevated WBC count might not be directly related but could be seen in the context of overall health status.

Sepsis: Although the WBC count is not extremely high, sepsis can present with a variety of white blood cell counts, and it's crucial to consider this diagnosis, especially if there are other signs of infection or organ dysfunction.
Hematologic malignancy: Certain blood cancers can cause both elevated WBC counts and abnormal liver function tests, including ALP. Missing this diagnosis could have significant implications for treatment and prognosis.

Wilson's disease: A rare genetic disorder that can cause liver disease and elevated ALP. While it might not directly cause a significant elevation in WBC count, it could be considered in the differential for elevated ALP, especially in younger patients.
Vitamin D deficiency: Can cause elevated ALP due to increased bone turnover. While not typically associated with a high WBC count, it's a condition that might be uncovered during the workup for these lab abnormalities.