Yes you can keep live clams overnight by storing them in the refrigerator in an open container on some paper towels.
The clams when stored in the refrigerator should last 3 to 4 days before they die or go bad.
If you already cooked clams then you can store those in the refrigerator in a sealed container and they should keep for a week or more.
If the clams are already dead and not cooked then you should not really keep them overnight as they could go bad and make you sick.
I have kept live clams though in the refrigerator overnight and they have been just fine the next day.