You can claim as many prompts as you feel you are capable of; if there are three prompts on one day that you think you could write/draw on time, feel free to claim all three. Currently there are no restrictions based on the fandom/date due of prompts, only on the number of claims per prompt (i.e. if three other people have already claimed a prompt for fic, you cannot write fic for that prompt).

Hope that clarifies things a little!