Whats the deal?
Take European ports that can send supply to SE France, multiply by four, this is your capacity for supplying your army. Now look at demand draw for your army, most easily done on the supply depot you have. If demand exceeds port capacity, you have your answer.
This happened historically, and Patton was denied supplies so that 21st army group could take more ports, and add supply capacity. You may need to execute an Operation Market Garden of your own.