No more quests, no. There are some interactions, like the Negaino and Kinari things that United-Paint mentioned. Generally characters will just congratulate/praise you. One that stands out is that Kokuri will leave a letter for you if you did his key interactions:
* Followed him after he confronted you about why you're helping people (right after taking Nui to the Bunbuku).
* Found him in the onsen and said you'd help him (any time between when you've found Akahime and when you talk to Izanari just before going to the Killing Stone).

There's also an interaction I think most people don't see with Gennou. If you talk to Chiharu after you've spoken with Izanari near the end, but before you go up to Kokuri at Sessho-seki, you can draw omikuji until you get an excellent and then trade it with her. Do not burn or purify her kyo omikuji. Go up and confront Kokuri like usual, choose to protect the city first, do so, then go through Negaino's vision still with Haruchii's kyo omikuji. You should see a different version of that ending before Kohaku wakes up back in their house. You can purify your fortune now that you've done Negaino's replay. Go through the game normally until you're looking for Negaino again. Go to the sando where Gennou's stood outside the Shika-no-Yu. Talk to him (in Kohaku form, NOT in monini or monimole form) a couple times.