^Not SpaceX. In fact, I can't think of any company that is. Who are you thinking of?
Despite it's name, the Falcon Heavy is not a "heavy" launcher. "Heavy" is generally applied to a launcher that can get in excess of 70 metric tons to orbit. Falcon Heavy is only projected for 53 metric tons.
I'm confuzzled. Last time I said I suspect that SpaceX are up to developing a heavy launcher if they get the opportunity, you countered me by saying they already have one.
I didn't mean Falcon Heavy. Note that I didn't say “already has designed and is planning to launch this year”. I said “interested in developing”. Based on their concept designs, Musk's personal goals for his company and some of his latter comments, he and SpaceX are definitely interested in developing such rockets whether there are any money in it for them or not. Whether they can develop them is another matter.
But given the price of the SLS program, the money NASA would pay for a deep space mission would probably be enough to fund such project.