One possible answer is heaven. (Another is seal.) The words all go with numbers:
- first aid
- third degree
- fourth estate
- Fifth Avenue
- sixth sense
- seventh heaven / seventh seal
You could create other puzzles with the same premise:
Of course, all of those could be amendment, or the first three of them could be base or degree or estate or world. But in most of the above cases I think the numbers given are the numbers most commonly associated with the given words.
You could also do a silly version of the puzzle:
But somehow I think it would be easier to guess the answer to that version.