Knowing where you are located would be very helpful. The overall growth pattern of the rhododendron - height, multiple slender trunks - suggests that it is receiving too little light which in turn suggests relocation as the best option. You will have to prune it to more manageable size, but rhododendrons are very easy to move because of their shallow, flat root systems. When to do this has a lot to do with your location. Wait until spring if you live in a cold winter area. If you live in the PNW or another winter wet, rarely below freezing area, moving now should be fine. You could, of course, prune and leave it where it is, but it will revert to its present state pretty quickly unless light is increased by taking out some of what is currently causing the shady conditions.

I am in the PNW and rhododendron is northern facing so light is definitely an issue...how much could I prune it prior to moving without killing it?

Pruning isn't at all likely to kill a rhododendron. You need to reduce the top growth enough so that the plant is not so unwieldy and top heavy. The photo seems to show new growth emerging near the base - a good sign that it will regenerate pretty quickly even with extensive cutting back. There are a number of online sources giving good illustrated instructions of where to prune on a stem for the best results. There are also good instructions for digging and moving. I would also check if this is indeed a good time for moving it in your area. I can't really think of any reason why it would not be, but my experience in the PNW is exactly 0. A good local nursery or your extension service can tell you.

IME, there isn't exactly a bad time to move a rhody here in the PNW :-) Although this past summer was certainly less than ideal. Now is a fine time to move one.

I would move it and then prune it into a multitrunked tree. Cut the smaller trunks before you move it.

Cut a ditch around rootball and rock it back and forth to get it up on a heavy duty tarp like canvas. Then drag it to it's new planting hole without skinning the bark. I would drag it by the tarp or rootball instead of attaching anything to the trunks.

Mike