Once a muscle is stimulated to grow from weight training, will extra sets stimulate it even more or will it grow the same amount since it has already been stimulated?
Yes, more stimulation (within reason) will lead to more growth. But there's a problem.
The more stress that a muscle undergoes the more nutrients and time are required for repair and adaptation.
So, say they you stimulate a muscle to grow and wait 2 days for recovery. You come back and you are stronger (that's the whole point right?). So you decide to do 2x the amount of work in order to get 2x the progress. You do that and come back in 2 days. Now you're weaker. You body has not had sufficient time to recover and build more muscle due to the increased stress. So you do it again, but wait 3 days. You come back and you're at the same point that you were 3 days before. So this time you wait 4 days. This time when you come back you are stronger.
But what really happened? Originally, you were going 2 days between workouts and you were getting stronger. So you were on a 3 day cycle. You can do 10 of those in a month. Now you go 4 days between workouts, that's a 5 day cycle. There are only 6 of those in a month. So, if your timing is perfect, you might get almost 2x as strong per cycle, and you might end up a little stronger in the end.
What's more likely to happen? You're more likely to under or over recover (decompensate) on various days and your results will actually be less than the original program.
It's hard to get it "just right". Doing a minimal amount of work ensures that you will recover sooner, you just have to do some experimentation to find out what works for you. And all of your muscles will not respond in the same manner. In general the larger the muscle the longer it takes to recover from a similar level of stress.
Do 10 sets of squats to failure and it could take a week for the quads to recover. Do 10 sets of arm curls to failure and you could be recovered in 2–3 days. It's all a balancing act and it's all unique to you.
Here are some charts that illustrate the recovery process: