There will be a time printed on your first FP telling you when you can get your next one. It's not immediate, so you normally won't be able to do what you're asking.
You CAN time your fast passes so that they fall close together if you are there during non-busy times or early in the morning. A few minutes after your window opens for your first FP ride, the window for getting a 2nd fast pass opens. We typically schedule our time so that we aren't standing right outside the ride when it is time for our FP return, so we check on other ride return times and snag tickets for something else so the clock is already ticking on that one when we go over to ride our first FP ride.
This wont work as well during busier times of the day because the return times tend to be too far away to make it as easy to do. You can certainly HAVE two fast passes like this, but the wait time for the 2nd will tend to be hours away from the first.
The maximum time you must wait before getting another fast pass is about two hours. Less if the park is not so busy. There have been some experiments where for some attractions (I think Lights, Motors at MGM is one of them) you can get another fast pass right away, although the next fetch time showing on your second (or third) fast pass would not be sooner than the next fetch time on your first (or second) fast pass.