Not much of a trick, but for the last steeping let that sit overnight, then consume the next morning. Be sure to cover it so that dust and bugs have more trouble getting in; the water jugs likewise get covered now due to a spider.
The tea should stand up to multiple steepings and should have a strong flavor: oolongs, pu-erh, maybe others. Anyways, it's an idea for tea where more steepings are possible but where drying the leaves is problematic (or you forgot). A warm kitchen may be a problem; a bit of salt, vinegar, or time in the fridge would help prevent anything problematic from growing. But that's getting towards a soup stock or maybe kombucha.
Cold brew coffee is also a thing, though the quantity of coffee required was somewhat discouraging. Maybe if you're trapped in a coffee warehouse without power and have nothing better to do with your time?