When you like DAI and Do As Infinity (I LOVE these two groups too, by the way!
), then you might want to give Onitsuka Chihiro, Sakamoto Maaya and Kalafina a try!
These are my favourite songs from them:
"Infection" by Onitsuka Chihiro
"Okitegami" by Sakamoto Maaya
"Lacrimosa" by Kalafina