Is there a serum level at which would provide the maximum anabolic response implying that any serum level higher at that point is just a waste or worse, contributing to side effects?
sure there is, POB's post #7 is exaxtly this. If he goes above 1.2g of test weekly he just gets added sides with very little if any benefit to anabolism or strength/gains in his case. What this serum level is I have no idea, blood tests could help verify it but I'd also assume it to be very dependent on the individual in question and the goals of that person.
Edit* An example from my last cycle is that in terms of fat loss I did not notice any difference between tren dosed at 400mg per week and 600mg per week. So if fat loss was my main goal I had reached the point of diminishing returns. My goal is strength and power though and I noticed a difference in those variables with the dose change so in that context it wasn't a waste. I guess it also depends on your viewpoint to a certain extent.
Once a serum level is reached and the subject grows accordingly, would the subject need to elevate that level to continue to grow?
It depends I think. If someone has maxed out growth on a certain serum level then yes you would probably need to elevate for continual growth. If you've just ran one cycle at 1g of test for example but didn't necessarily max out your growth on that equivalent serum level then you'd probably be able to continue growth on the same dose. We know AAS increases the rate and amount of protein synthesis while also inhibiting proteolysis but that doesn't mean you've maxed out growth on a 750mg per week cycle of test just bc you did it for 16wks. There might be more growth potential at the same dose, there might not. It depends on your starting point and how efficiently you ran your cycle, how long it was, how your training was, and so many other factors.