That's safe. Unless maybe you quote bits word for word, parody is a legal defence against copyright infringement claims.
The answer to your basic question is "Yes." See Airplane!, Bored of the Rings, Pride and Prejudice and Zombies, Goodnight Dune, pretty much "Weird Al" Yankovic's entire music catalog...
edited 5th Dec '14 7:34:49 AM by Madrugada
...if you don’t love you’re dead, and if you do, they’ll kill you for it.It might be worth remembering that with Airplane!, the studio that made it already had the rights to Zero Hour, so copyright wouldn't have come into it (it lifts dialogue and other things almost wholesale, so it might have been crossing the line a bit otherwise).
edited 5th Dec '14 8:22:46 AM by Bisected8
TV Tropes's No. 1 bread themed lesbian. she/her, fae/faer...and Weird Al often asks permission from the original songwriter as a courtesy, and Pride And Prejudice is in the public domain.
But the answer is still yes.
The Revolution Will Not Be Tropeable
I was thinking of self publishing a trilogy of books on amazon to be a parody of Twilight with some Buffy mixed in for flavor. Was gonna follow the plot more or less with a few twists and lots of humor and, well, parody/satire. And the vampires start out normal and the conflict is about then becoming diamond skinned abominations. Would I be safe from copyright infringement under parody, since it's not intended to be plagiarism?