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 think of is pretty far-fetched. Does anyone know what I mean better than I do?