The short answer is that there are a lot of variables, so your process has to be dialed in per bean, which is why most people end up just sticking with 1 type of beans.
Different roast levels are going to have different densities. Different bean varieties (and localities) are going to have different density and size. The age of the bean comes into play as well.
Some variables affect the actual brewing, others affect how the beans grind. Every once in a while, i'll have a bean that just seems to make more fines for whatever reason. I guess it's just down to the stiffness of the bean and the size.
If you want to be able to switch beans at will, you'll need to keep notes for each variety, and adjust back and forth as needed.
I don't think you'll be able to get a new bean right on your first shot no matter how you try to adjust. If you adjust for one variable, there's still all the others.