PFC Randolph R. Greco, 32 844 753, Army of the United States, is buried at American Battle Monuments Commission Netherlands Cemetery, Margraten, Holland. He was living in New York State at the time he was drafted into the army. It's anybody's guess as to where he was actually from.
You already have all or most of the above info. I assume you've been to the cemetery (and his grave) - quite possibly where you'veobtained what information you have. There's a better-than-average chance his immediate family - parents, brother(s), sister(s) - are deceased.
I can trace living relatives but it will involve expenses that I must pass along. This sort of research is becoming increasingly difficult (read: costly). Very often costing more than the info is worth - but that's your decision. Also, I can't assure that relatives will be willing to communicate with you.
Just recently I did a search for relatives of a man the client - a war baby - claimed was her father. The family was terribly upset and refused to communicate with her and threatened to sue ME for giving her their address and phone (this, of itself, is no big deal - I don't know how to act if there aren't at least ten people threatening to sue on any given day).
Very often, it's entirely different - all concerned are overjoyed at having found a new sister, brother, cousin, etc. Think it over and let me know if you decide to go with it.
In the meantime, you can use his name and service number (above) to order his deceased file. You'll find instructions at Message #2112. Go back to the Main Page, enter "2112" in the box in the upper right corner marked "Jump to #_____" then click on "Go".