If I remember correctly, for players with the old Ch. 1-5 tech tree the Spire is:
Ch. 3-4 - 1 star
Ch. 5-7 - 2 star
Ch. 8-up - 3 star
This is true for the entire Spire, and they do not change as you progress upward through the floors.
I have no clue what it looks like for those with the new tech tree where they don't get the Spire in Ch. 3.
Tourney is linked to province number:
Provinces 1-5 - 1 star
6-10 - 2 star
11-up - 3 star
As far as I know, 4 star enemies have not appeared in the game as of yet.