Driver shield providing 24+ pins at 100mA (for Mega 2560)
You can:


use a driver chip, e.g. ULN2803 which gives you 8 outputs of up to somewhat 500mA from 8 digital pins 
use a serially addressible power+logic chip, such as TPIC6A595NE which gives you 8 outputs, each can drive 350mA, and has a built-in short circuit protection. You can cascade these, 3 chips give 24 outputs, and need only three pins to drive all 24 (or more if you use more chips) outputs.
There are 24 output devices, however not in this current range. 24 output devices are usually i2c or spi based led controllers - some of them gives you goodies like rock solid hardware PWM on all 24 ports - but none of them gives you 100mA output.