aye, the trick is that they will help each other *if it is in their own interests to do so*. This can include long-term interests. That said, if it is in their own interests to openly betray an "ally", they will do that (Cue: "I believe the usefulness of our partnership has come to an end...Good-bye!" (kills "ally"). If it is in their own interests to *secretly* betray an "ally", they will do that. Thus a sneaky good guy just has to give one of the evil allies the convincing impression that it will benefit by betraying its allies, and it will do so.
I would suggest that LE folk are more likely to see the "big picture" and work together than NE folk, who in turn would be more likley to work together than CE folk.
That said, good folk ally with each other more easily than evil folk, for the simple reason that good folk have both the motivation of self-interest *and* the motivation of helping (and not betraying) their allies as reasons not to betray their allies. So evil folk would be allied less often than good folk, other things being equal.
So I would think that, in order of "working together", the most likely would be LG, then LN (there are less beings they would consider allies, but they would be loyal to those allies), then NG, then N, CG (not that organized, but recognize that others need help), LE (enlightened self-interest + a love of organization), NE (just enlightened self-interest), CN (the "leave me alone"/early "Han Solo" alignment), CE (combines "let me do what I want" and "self-interest", so it is very hard to maintain "enlightened self-interest" for long). IMHO.
For an example of evil folks working together, read Villains by Necessity, by Eve Forward. Note the extreme circumstances required to keep the villains from turning on one another.