Let's turn the cheese up to 11!
The main limitation on sneak attacking outside of your turn is that pretty much every way of making an attack outside your turn requires that you use your reaction, limiting rogues to sneak attacking twice per round. The only way I know of making off-turn attacks without spending your reaction is the Tunnel Fighter fighting style from Unearthed Arcana, which says:
As bonus action, you can enter a defensive stance that lasts until the start of your next turn. While in your defensive stance, you can make opportunity attacks without using your reaction
With this ability you can potentially sneak attack every turn if an enemy obliges by triggering an opportunity attack. You can't usually expect enemies to be so helpful, but there's a way around it, the Polearm Master feat, which says : While you are wielding a glaive, halberd, pike, or quarterstaff, other creatures provoke an opportunity attack from you when they enter your reach.
The feat doesn't actually require you to make the opportunity attack with the polearm you are wielding, so if you wield a quarterstaff in one hand and a rapier in the other, you can make an opportunity attack with the rapier against any enemy that enters your reach, triggering Sneak Attack if you hit. If you have the tunnel fighter stance active your can do this to every enemy that enters your reach, potentially sneak attacking many times per round!
I would never allow this at my table since it relies both on an optional rule from UA and a highly questionable reading of the PM feat, but it is fun to speculate
The main limitation on sneak attacking outside of your turn is that pretty much every way of making an attack outside your turn requires that you use your reaction, limiting rogues to sneak attacking twice per round. The only way I know of making off-turn attacks without spending your reaction is the Tunnel Fighter fighting style from Unearthed Arcana, which says:
As bonus action, you can enter a defensive stance that lasts until the start of your next turn. While in your defensive stance, you can make opportunity attacks without using your reaction
With this ability you can potentially sneak attack every turn if an enemy obliges by triggering an opportunity attack. You can't usually expect enemies to be so helpful, but there's a way around it, the Polearm Master feat, which says : While you are wielding a glaive, halberd, pike, or quarterstaff, other creatures provoke an opportunity attack from you when they enter your reach.
The feat doesn't actually require you to make the opportunity attack with the polearm you are wielding, so if you wield a quarterstaff in one hand and a rapier in the other, you can make an opportunity attack with the rapier against any enemy that enters your reach, triggering Sneak Attack if you hit. If you have the tunnel fighter stance active your can do this to every enemy that enters your reach, potentially sneak attacking many times per round!
I would never allow this at my table since it relies both on an optional rule from UA and a highly questionable reading of the PM feat, but it is fun to speculate
