EVP:
I'd use some of these http://www.ti.com/lit/ds/symlink/tlc5940.pdf
Looks interesting but I can't figure out what current they can handle.
The 60mA(For Vcc<3.6V) or 120mA(For Vcc>3.6V) refers to the current for one channel or all 16 channels?
If the 120mA limit is for all channels it means I can only use 6(I need 20mA per channel) channels at the same time which won't be enough.