It can be done I'm sure but it would probubly be more of a pain in the butt than it's worth. We're talking--is the route already there? Circuit board --need new one? The cost to have someone do a job like that would not be cheap and who knows how long they would have it? If you do it yourself there is no warrenty on the job. I paid 100 bucks just to have a luthier (spell check) drill 5 holes in a Strat body for a bridge! I had no choice. BUT as soon as I say all that some guy will pop up and do it for nothing and that blows my theory out of the water again. Who knows...it may just be easy?
If you sell your single H and purchase an HS model, you will be much happier. It probably won't cost any more than a professional conversion by an experienced Luthier................If you try and do it cheaply, you will just make a perfectly good Sting Ray a "Franken Bass"!
Its defiantly possible but as mentioned you will end up having neither one thing or the other.
Have seen a conversion before on a SR4, there was an extra H added in the neck position with the original Single H still in the sweet spot and operated by a blend pot, it sounded quite nice but how it was done ??? no idea.
Just trade it in for a HS model, be much more simple.