I would also tend to say, "I need two more..." unless whatever was being requested came in groups of two, so that there was no possibility of asking for one more or three more. In that case, "another two" would be somewhat more likely, although "two more" would still be possible. I've been trying to think of an example to illustrate this, without much luck -- every situation I can
Okay, here's an example. Suppose a couple is having drinks in a bar and the man (out or chivalry or chauvinism, whichever) is ordering drinks for both of them. After the first round of drinks, he might ask for "another 2 martinis" rather than "2 more martinis," because he's thinking of them as "another group of two."