Hello - it sounds as though the presenting symptom here is weight-loss, with vomiting and diarrhoea. Typical illnesses that present like this include
- hyperthyroidism - this is diagnosed on blood-tests, but not every vets office runs it automatically - sometimes it has to be specifically requested
- pancreatitis - inflammation of the pancreas, presents as weight-loss and vomiting, often involves abdominal pain but this is difficult to pick up from the outside of a healthy cat
- cancer eg lymphoma (but various possibilities)
- foreign bodies of the stomach
- liver disease
- inflammatory bowel diseases
- diabetic ketoacidosis - should show on bloods but some old blood machines miss out glucose
- toxicity (check recent diet indiscretions as some toxins to cats are surprising)
- partial bowel blockage
- infectious diseases e.g. Giardia, worms, FIV, FeLV etc.
There are more. Your vet should make a differentials diagnosis list more specific to your cats' particular set of circumstances and go about ruling them out. Meanwhile, your vet will want to regularly assess his hydration; he may need a drip to support him. It sounds as though your vets may already be part-way through this process and a good way to discuss it would be to ask what the differentials (possible diagnoses) are, what has already been ruled out and what needs to be done to rule out the next most likely thing. If your vets don't know, they may consult a specialist as regards working out the next step. I hope that something there is of use.
Best of luck with everything