Final answer:
The patient's symptoms of hypercalcemia, normocytic anemia, and proteinuria with Bence Jones proteins indicate the likely diagnosis of Multiple Myeloma, a type of blood cancer involving abnormal lymphocytes.
Step-by-step explanation:
The patient's clinical presentation suggests that the most likely diagnosis is Multiple Myeloma. This is indicated by the laboratory findings of hypercalcemia, normocytic anemia, and proteinuria with the presence of Bence Jones proteins. Multiple Myeloma is a hematological malignancy characterized by the excessive division of lymphocytes producing immunoglobulins, leading to the excessive excretion of Bence Jones proteins, which contain abnormal light chains of the immunoglobulin molecules. Additionally, Multiple Myeloma can affect kidney function through mechanisms like "cast nephropathy" and can lead to elevated serum protein levels that show distinct bands on protein electrophoresis.