Fifty two year old woman is admitted with a humeral fracture following minimal trauma. Biochemical investigations included a bone profile, including plasma phosphate and magnesium, the results of which are shown below. X-ray of her humerus reveals osteolytic lesions in addition to the fracture.

Total calcium 3.28 mmol/L (2.20-2.60)

Adjusted calcium 3.38 mmol/L (2.20-2.60)

Phosphate 0.42 mmol/L (0.7-1.4)

Albumin 42 g/L (35-50)

Alkaline phosphatase 532 U/L (30-130)

Magnesium 0.73 mmol/L (0.7-1.0)

(a) Suggest a differential diagnosis for this clinical presentation (200 words)

(b) What further investigations would be appropriate? ( 200 words)