1. (particle) please - implies entreaty and is used with requests to soften them and to make them more polite.
Homai koa te miraka. / Pass the milk, please.
E hoa, kau mai koa ki konei nā (NM 1928:101). / My friend, swim over here, please.
(Te Kākano Textbook (Ed. 2): 63, 111;)
2. (particle) indeed, in fact, really - used to intensify and add emphasis.
Kāti koa nō te 1 o Hūrae o te tau 1971 i mate ai a Īhāia Puketapu (TTR 2000:167). / Well in fact Īhāia Puketapu died on 1 July 1971.
3. (particle) but, however,on the other hand, despite that.
I māmingahia e ngā kaihokohoko, riro ana ngā whenua hei utu i ngā nama. Ehara koa, i ū tonu tana tautoko i te Pākehā (TTR 1990:285). / They were tricked by the traders and the lands were taken to pay the debts. despite that, his support of the Pākehā continued.