Is it that the drive is faulty or deleted data that is too disorganised for the usual utilities (eg piriform recuva).
If you are talking about opening up the drive and you really need the data you are talking about someone like Seagate Seagate
but you are talking about big bucks.
I have used another company in the past but can't remember who it was and too many are coming up in google to trigger my memory.
Last price I heard of was £2000 for deep level (though the data was worth much more than that and it was urgent), highest price where I've actually known the customer was around £800. Could well be cheaper or dearer now, there are a lot more in the market. I also know a few people who have paid around £200 with successful outcomes.