You can use pretty much any hair dye on a hair system. You don't need to use hair dye specifically designed for a hair system. Just be careful if using permanent or semi-permanent hair dyes - do a patch test first to check the colour is correct and try to avoid getting the hair dye on the base.
As above, any mainstream brand seems to work for me. 2 things to be cautious about is dye on the lace esp at the front.
Also if you are dyeing to match your native hair, maybe wear and dye both system and native to give a close match