Primary Hyperparathyroidism: This condition is characterized by the overproduction of parathyroid hormone (PTH), which leads to increased calcium levels in the blood. Elevated PTH also increases phosphorus excretion in the urine, but in some cases, especially with significant bone resorption, phosphorus levels can rise. Low magnesium levels can be seen due to increased renal excretion induced by high PTH levels.

Vitamin D Intoxication: Excessive intake of vitamin D can lead to increased absorption of calcium and phosphorus from the gut, resulting in elevated levels of these minerals in the blood. Magnesium levels can be low due to secondary hyperparathyroidism or increased urinary excretion.
Malignancy-Associated Hypercalcemia: Certain cancers, such as multiple myeloma, lung cancer, and breast cancer, can produce substances that mimic the action of PTH or directly stimulate osteoclast activity, leading to elevated calcium and phosphorus levels. Low magnesium levels can occur due to increased renal excretion or tumor effects.
Familial Hypocalciuric Hypercalcemia (FHH): This genetic disorder leads to an abnormal calcium-sensing receptor, causing an inappropriate secretion of PTH and subsequent hypercalcemia. Phosphorus levels can be elevated, and magnesium levels can be low due to the effects of elevated PTH.

Hypercalcemia of Malignancy with PTHrP (Parathyroid Hormone-related Protein): Although less common, this condition can present with similar laboratory findings and is critical to diagnose due to its association with underlying malignancy.
Sarcoidosis: This autoimmune disease can cause an overproduction of vitamin D, leading to increased absorption of calcium and phosphorus. Although magnesium levels are not typically low in sarcoidosis, it's a critical diagnosis not to miss due to its systemic implications.

Familial Tumoral Calcinosis: A rare genetic disorder characterized by hyperphosphatemia, which can lead to secondary hyperparathyroidism and elevated calcium levels. Magnesium levels can be low due to the effects of high phosphate levels on renal magnesium handling.
Hungry Bone Syndrome: Although typically seen after parathyroidectomy, this condition can occur in other settings where there's a rapid change in calcium and phosphate homeostasis, leading to hypocalcemia initially but potentially hypercalcemia and hyperphosphatemia as the bones "hungry" for minerals take up and then release them. Magnesium levels can be low due to increased uptake by bones.