You have two options:
1) Render in layers to reduce the memory requirements per render. You then composite the image together when you've rendered everything out.
2) Simplify the method you're using to make it simpler and quicker. And there are probably dozens of techniques you can do.
You can get good results using texture mapped hair (you get the same results that you seen on recent in-game CG. You can see it here:
http://www.virginmedia.com/microsites/games/slideshow/finalfantasy12/img_21.jpg ) but I find that adding transparency, which is required for that extra realism, ups the rendering time
massively, especially if it they cast shadows - your rendering engine needs to calculate how much the light is being retarded by each transparency map and when you have a dozen layers of hair, this is pretty damn awkward for it. And if you don't cast shadows, well, there's no point in the transparency map because the hair won't have the depth and it doesn't look good.
Another option is to go for pure polygonal hair that is extruded by a displacement map, the rendering is made more efficient with Lightwave's APS but I don't know what the equivalent is with Max. Again, the rendering time increases with adding transparency, you're also usually limited to fairly straight hair, but it works great for fur.
You can see my attempt to stretch it out here: