Like FJK said, with the stock setup it will be able to properly drive only one LED.
However, if you want to pick up the challenge and rebuild the internals from scratch, you may have this solution to run the three dices.
- replace the stock battery holder with a single 18650 lithium battery
- replace the six transistors on the MR board driving the LEDs with a single high power transistor
(it`s just the same approach used to convert the Hasbro economy boards)
You can find some detailed info in this old post
Pyros, a custom "Dual-Phase" Mace Windu conversion
With that setup I was able to feed the LEDs with only 1600mA, but the limitation was coming from the NiMh batteries I had to use.
Using a good 18650 Li-Ion battery you won't have this limitation and you may be able to feed up to 1000mA for each die.