A Kohen has to just seperate Tremah but he can eat it himself and he has to give Ma'aser to a Levi. Can Kohen go and give much more than nessecary for Terumah so then when he takes Ma'aser from the leftovers he has to give less?
Actually, a Kohen does not have to give Ma'aser to a Levi. This is derived by Chazal in the Sifri (Bamidbar Parshas Korach ch. 18, #61) from Bamidbar 18:26, "And speak to the Levites....when you take from the children of Yisrael the Ma'aser....". The Sifri learns from this that Yisraelim have to give Ma'aser to the Levi'im but Kohanim do not have to give Ma'aser to the Levi'im.
The Sifri continues that since Kohanim need not give Ma'aser to the Levi'im I might think that they can eat it as "Tevel" - without having to separate anything from it. Therefore we learn from Bamidbar 18:28, "So shall you also lift up the Terumah of Hash-m", that the word "also" comes to include that the Kohanim must also separate Terumah.
This is cited as Halachah in Shulchan Aruch YD 331:68 - that Kohanim must separate Terumos and Ma'asros and they keep it for themselves. Shulchan Aruch 331:69 also states that one may not take the Ma'aser out of the hands of the Kohen.