It is possible to load multiple copies of the same version after effects, but unfortunatly it won’t allow you to copy and paste between them.
I’m using Windows 7, and a second copy can be opened by opening a command prompt and typing:
“C:\Program Files (x86)\Adobe\Adobe After Effects CS4\Support Files\AfterFX.exe” -m
I don’t see much point in forcing it to do this though since you can’t really work between them very well, and a single After Effects is enough of a resource hog as it is.
One way you can copy and paste effects from one project or another without importing is to copy and paste a single effect or layer. First open the first project, select the effect or layer you want to copy (Preferably by going to Edit>Copy instead of using the keyboard shortcut), loading the second project, and using Edit>Paste. The disadvantage of this is you can only copy one effect or layer at a time, and alot of the time I find that doesnt even work that well. Also, it won’t copy the source material along with (even solids), so most of the time it will immediatly turn up bars and say “Source Deleted”.