Is Facebook offer negotiable without competing offers?

Of course.

Or you could just.... lie.

There is always the secret final weapon. “If you add ___ to ___ , I will accept. Otherwise I will need tome think about it.”

"the offer looks okay but I was looking for a higher {base/equity/sign-on} for my next move, as I have some upcoming expenses that need to be covered." Make sure you're clear that you have a viable alternative, including staying at your current company or taking longer to think and decide (or even doing more interviews). It's in their favor to increase the offer if it will get to there faster

You can negotiate if you are ready to walk away from the offer. If all of your interviews were strong hire signal, you might have the leverage.