The most likely explanation for this patient’s polyuria is hypercalcemia.
With severe hypercalcemia, Ca2+accumulates in the inner medulla and papilla of the kidney and inhibits adenylate cyclase, blocking the effect of ADH on water permeability.
Because ADH is ineffective, the urine cannot be concentrated and the patient excretes large volumes of dilute urine. His polydipsia is secondary to his polyuria and is caused by the increased serum osmolarity.
Psychogenic water drinking would also cause polyuria, but the serum osmolarity would be lower than normal, not higher than normal.