Here's > 240 mA through LEDs, approx 14 mA ea., via PN2222A.
These transistors cost < 10 cents.
That all should be self-explanatory.
The DVM readings in the following demo are just a wee bit off from those in my schematic (above) as, in between, I was working with something else and didn't dial back the supply exactly - so sue me.
I use a jumper [ J ] to switch between 1 LED and 20.
Even with V_ce = 300mV, device dissipation is < 100 mW.
There's no precarious balance going on, it's a solid performer.
Party On.