The max likes with Harold depend on if you top him or bottom for him (higher Brave or Lewd fame). The overall max seems to be 36, if you bottom for him.
Hyao has changed the fame designations to Brave and Lewd. The highest Lewd score in Bareshade is 17. You must NOT "Relax" at the Tavern until your Lewd fame is exactly 15. When you do, there is a high random chance you will get 2 points if you give in to the Drunkard (it appears to be a first time and one time only event, best I can tell).
If you do this at 14 points or below you will stop at 16. If you do this at 16 you will get no more points, If you do it at exactly 15 points you will get 17 points.
There is no real benefit to getting 17 points, 16 will keep your Lewd fame higher than your Brave fame, so far.