I'm not an archer, but I saw this and thought it was cool:
Ignoring the fact that it's magical, are bows with 4 or more limbs and 2 or more strings possible in reality? Would there be any benefits?
Absolutely. In fact, there are bows out there like this with two limbs and two strings. I have had the opportunity to fire one of these bows and came up with a few results at the time. At arms length requires twice the effort and pounds in order to pull the bow back, however you get double the distance and impact power. Due to having two limbs, it also has more force than a much larger bow, offering more power in a smaller form. There are many benefits and the design is actually quite simple when you break it down.
It could be possible if you use something elastic.
You would just have to graph it like a slingshot, elastic x-shaped, having a hole in the center of the Bow where you can shoot the arrow through.
You would just need an area to shoot the bow from, it doesn't necessarily have to be in the middle, it can be off to the side a bit, like most bows.
I was just designing a shape for this kind of bow. In my opinion you would be able to cross 2 limbs which cross-outwards more the hard you pull the string. Also, if you use regular bow-rope instead of elatics like mentioned in another reply, you would need to have a pull-object which keeps the ropes crossed in one place. ^^ That's my take on it.