Do Social Link points stack past the required amount for the next rank?

While on summer vacation, I had a lot of free time to improve my relationships. However, I discovered that Yusuke apparently really likes the coffee at Cafe LeBlanc, since he came over 4-5 times in 10 days. Since I'm only rank 2-3 with Yusuke and spending time with him leveled up my Charm, I accepted all his invitations.

I know for a fact that I accumulated more than enough points to level up my Social Link with him once, so the next time I hang out with him, his Social Link rank will increase.

However, will all these points I earned carry over to the subsequent ranks? That is, will I still need to hang out with him a couple times before I can level up his Social Link again or will the points I earned during our summer break allow me to immediately rank up with him again?

Solution 1:

Having tested by using the fortune teller ten times with a corresponding Persona before progressing a low-level social link, I can confirm that the points do not stack past the current S-Link level's requirement.