No, it is NOT possible to get too much dialysis. There is no such thing. Healthy kidneys work 24/7, and provide a glomerular filtration rate (GFR, or level of kidney filtering) that is normally about 90% or greater. By way of comparison, even good PD might get you about 15%.
It IS possible to remove too much water, though. Dialysis removes wastes, and it removes water (ultrafiltration). Getting too dry (being dehydrated) makes you feel pretty wretched.
You said that after Anthony's PD dose was reduced (why they would do this when he was doing well, I can't imagine), he felt "Loss of appetite, nausea, food tasted strange. So he went back on 8000 ml, but further tests showed fluid around his heart." All of those symptoms--including the fluid around his heart--are signs of underdialysis. Or, they could be caused by something else. We're not doctors, but the "food tasted strange," in particular REALLY makes it sound like uremia. Did you by any chance notice that he had ammonia breath when this was happening?
My guess is that reducing his PD dose that first time destabilized his whole system. He became uremic, and it's been an uphill climb to try to get back to where he started out. Getting more protein into him may help. Talk with his dietitian about his blood protein (serum albumin) level, which should be 4.0 g/dL or more, if possible. There are tasteless protein powders that can be added to foods.
It may also be that he needs more waste clearance than he can get with PD, and switching to a form of home hemo that is every day or every night might help him feel much better. He is most definitely NOT getting "too much" dialysis, though.