I've got a few home rules I've used for years.

1. Healing Potions: Drinking is a bonus action, using an action player gets the max value. Potion can be thrown 15 ft to a downed target as a bonus action, DC 10 DEX check, brings target to 1 HP. Thrower can choose to spend an action to throw the potion, then they have to pass a DC 12+1 DEX for every 5 ft from target, but if they pass target can roll the healing.

2. Team inspiration: Group shares a pool of inspiration. Up to a max of 5 that can be used at anytime.

3. Inspired saving throws: Players can spend their reaction and a point of inspiration to gain a saving throw re-roll.

4. Initiative Swap: Allow the players to swap initiative rolls with one another before combat starts. Sometimes players have an idea that requires teamwork based on a specific order they’d like to act in, and this allows them to always get the order they want.

Additional smaller rules:

A) Anything you can do.... can be done to you.

B) Roleplay can give modifiers to any roll, or can negate critical hits/success.

C) Every interaction is a chance to roleplay.

D) Once combat begins, diplomacy becomes much harder.

E) When leveling Up, Players can roll or take the average HP, whichever is larger.

F) At Player level 1, Player can take a feat.

G) Caster can spend 2+1 hit dice to recover 1 spell slot up to lvl 3 during a short rest. Can gain additional level for an added hit die per level up to 5th.