Kind of a loaded question...you can always have at least one in your possesion, and depending on your window at least two.
The scenario for two: You get a fastpass for Space Mountain at 9 AM with a return time of 10 to 11 am. At 10:01 you go to Buzz and get a new fast pass, at that moment you've got two FPs.
For more than two...grab all you can when the window opens for your next one. You can generally use expired fast passes with no problem. Meaning, you use that SM FP at 3PM rather than between 10 and 11. In that sense, you can hold multiple fastpasses until late in the day.
"Legally" there's no limit on how many you can have at once, you just need to get one as soon as your window opens. I suppose depending on the timing of your attractions you could easily have three or four.