Not variants, but I have 2 home brew rules I use:
1. Alternate falling damage. This makes falling short distances slightly more risky than normal, and keeps falling as a serious issue at level 20. You look up the distance fallen on a table for the damage. The creature may make a Dexterity (Acrobatics) check as a reaction to mitigate the damage by the value of the check. Jumping down as part of your movement gives you advantage on the check. This means a commoner has as much chance of walking away from a 10-foot fall as dying from it. And 1,500-foot falls will splatter low-level characters, but high-CON heroes, raging barbarians, and monks will be able to walk away with some of their hit points remaining.
http://www.enworld.org/forum/rpgdownloads.php?do=download&downloadid=1410
This made for some high excitement in our campaign a few months ago. The party came under attack as they came upon a damaged bridge crossing a 60-foot chasm. The bottom of the chasm was full of brush that was on fire except for a cart that was a small island in the fire. The monk decided to Dash across the bridge and missed seeing a weak spot that crumbled under him. He failed his Dexterity saving throw to keep from falling. He rolled low on his Dexterity (Acrobatics) throw to mitigate the falling damage. The 60-foot fall did 45 - 10 damage, and the level 3 character was knocked unconscious...in the burning brush...on fire. The bard Dashed across the bridge to the hole and cast
healing word on the monk. The monk got up, and the fire damage was low enough that he did not fall unconscious again. He was able to climb out of the fire onto the cart and put out the flames on himself. After the battle, the heroes hauled him back up to the bridge.
2. Matt Mercer's resurrection rules. Outside of
true resurrection, coming back from death is not automatic. The healer must make an ability check to bring the creature back from the dead, but other creatures may contribute to that check. Coming back from the dead was a bit too easy in my last campaign, so I am giving this a try. The heroes are being
very careful not to die this time around as death might be permanent.
https://geekandsundry.com/use-critical-roles-resurrection-rules-in-your-own-campaign/