Kidney Stones - What's the diagnosis?

A 65yo man was reviewed in the clinic for assessment of kidney stones. He has a history of stones for at least 8 years and has been passing small calculi on a regular basis for the last few months. His 24 hour urine results are shown below (results are 24 hour total values unless otherwise specified):

Volume, Liters	0.71	Sodium, mmol/day	7
Supersaturation Calcium Oxalate	10.11	Potassium, mmol/day	45
Calcium, mg/day	78	Magnesium, mg/day	52
Oxalate, mg/day	28	Phosphate, mg/day	0.76
Citrate, mg/day	11	NH4, mmol/day	68
Supersaturation Calcium Phosphate	0.71	Chloride, mmol/day	48
Urine pH	5.6	Sulphate, mEq/day	39
Supersaturation Uric Acid	2.71	Urea Nitrogen, g/day	11
Uric Acid, mg/day	0.499	Protein Catabolic Rate	1.2
Creatinine	1292

He has a high risk for calcium oxalate and uric acid stones. His urine citrate and sodium are remarkably low and he has a very low urine volume. His BP in the clinic was normal as were his labs apart from a serum creatinine of 1.3mg/dl

What is the underlying diagnosis (an important  piece has been left out of his background history)?
What is the best approach to treating his kidney stones?

Answers in the comments please (if this proves popular we may make it a regular feature).