can you re-ice cream ice cream soup?
Yes, absolutely. Restaurants do this all the time. In fact, it's recommended to re-spin the ice cream nightly because once it's reached serving temp, if you return it to the deep freeze it can crystallize and get nasty. Best to let it melt down and re-spin.
The texture may not be exactly the same as the original, but it'll still be ice cream.
By the way, if your ice cream has been sitting in your freezer for too long and has been through too many defrost cycles, and is starting to form ice crystals... this is a good idea as well.