Been thinking a little bit more about an expanded Affinity System as I detailed in a different post in
another topic.
A high affinity rating with Shenhua could unlock the ability to give her herbs to sell at higher prices than Ryo would get in the shops (because she's cuter, obviously), and also a mechanic where if you bring her ingredients she'll cook you a meal that confers XP boosts and temporary stat bonuses. Maybe you can also buy her recipes to unlock more dishes?
Tangentially related, but I was also thinking about a rent system in whatever domicile Ryo, Shenhua, and Ren are staying in during Shenmue IV. In my fantasy version of Shenmue IV, Shenhua picks and sells herbs for an income and reliably pays her share of the rent even on low to medium affinity, while Ren gambles his money and will only pay his share intermittently unless you have a high affinity with him.
Not paying your rent in a reasonable time will lose you affinity with Shenhua (let's say it's a weekly thing rather than daily), and activate some hidden events escaping from debt collectors if Ryo goes into arrears. If you don't pay rent at all during the game, maybe on completion you get an achievement or some special item/piece of clothing for repeat playthroughs.
I'm not sure how "Shenmue" this would be, but now the cork has been popped on New Game Plus modes in the series, I wouldn't mind a ranking system that tracks certain player statistics and lists them off at the end. Like the aforementioned non-payment of rent might get you the "Freeloader" stat (plus bonus item/clothing piece), or completing the game in under a certain time might net you an "Efficient" stat. The kernel of the idea comes from Metal Gear Solid of all places, where they'd give you the end of game ranking screen and unlock new items and weapons for repeat playthroughs.