This is for GMs only. Begone players, I say! Begone!
I ask only because Book 1 only provides information regarding influence checks made during social rounds, not attempts to improve attitude via Diplomacy checks.
Every character has a section in their influence statblock called "Successes Needed". This is the number of successful influence checks needed to increase their attitude by one step. So if the PCs make 3 successful influence checks on an indifferent character with 3 Successes Needed, they'll go from Indifferent to Friendly. Another 3 and they'll go to Helpful.
The books pretty much assume that you don't use Diplomacy checks to influence people, or at least don't really account for it. Once a character has or hasn't been influenced, that's it (at the Gala at least; the Jubilee has rules for later interactions). If you wanted though you can have players use downtime to correspond with these characters, thus giving them more rounds to make influence checks against them.