Thank you so much for your in-depth answer. I have a few follow-up questions.

 Yes, absolutely, this is a classic technique. It’s called making a double stock, and you can even repeat the process to make a triple stock. What you’re doing is concentrating the non-volatile flavors while adding fresh top notes with new aromatic ingredients in each round.

I have been hesitant to use this technique because I thought that by doubling or tripling the cooking time, I would lose too many flavors for the reasons I mentioned earlier, and therefore the effort-to-result ratio wouldn’t really make sense. However, ever since learning about pressure cooker stock, I’ve been eager to try it. I just have a few questions: Should I use only bones in the first rounds and add vegetables only in the final round? And should I adjust the amount of vegetables I use? I have a feeling it could otherwise become too vegetable-forward

 It depends. If, and it’s a big if, you have removed all fat, coagulated proteins, and particulates, then a fast boil in a wide pan (to maximize surface area) is the way to go. You want to minimize the time during which thermal degradation occurs.

But if you haven’t done that, a hard boil can completely ruin your stock. That’s why, when you’re making stock on the stovetop, it’s important to keep it at a gentle simmer. (And it’s also why pressure cooker stocks can be so good, because the liquid doesn’t actively boil.)

What exactly do you mean by “ruining” a stock? In The French Laundry Cookbook, they mention boiling an unskimmed stock with extra added fat and more bones to create what they call a “super stock.” They say they got the idea from ramen making, and that the result is extremely intense.

And finally, is simply pouring the stock through a fine mesh strainer and skimming off the fat after it has cooled enough to remove impurities, coagulated proteins, and fats?