The general multiboxing recommendation would be to aim somewhere between the wow minimum and recommended specifications *per character you want to multibox*

So that's 2-4 cores/threads on your CPU per account, and 2-4GB of video card RAM per account and 2-4GB of system RAM per account. So to multibox 4 accounts, we'd recommend an 8-core/16-thread CPU, 8-16GB video card RAM and 8-16 GB of system RAM just for WoW - not counting Windows and whatever else you're running at the same time (so add some extra CPU and system RAM to account for everything else).

You can cut back on video RAM a bit by turning down graphics settings, but you'll still want as much video card RAM as you can get, at least a high end 8-core CPU and 16GB system RAM at a minimum - 10+ core CPU and 32GB system RAM would be better.