possibly

(modifying a clause or predicate) Perhaps; indicates that the proposition may be true (is not certainly false) regardless of any facts or circumstances known to, stated by or implied by the speaker.

"It was possibly the costliest mistake in the organization's history."

(modifying a verb) In the realm of possibility; indicates that the action may successfully be performed (is not impossible) regardless of any facts or circumstances known to, stated by or implied by the speaker that might limit the performance.

"I couldn't possibly be there on time."