Welcome to the forum. Just to clarify, you have a completed Drawing of a model, the model has more than one configuration, and now you'd like to make a copy of your existing Drawing and have it reference a different configuration of your model? If yes, it's pretty simple. Save the Drawing to a new name, click on the drawing view of the model to show its Property Manager, and choose the other configuration from the drop-down shown below. That will change the drawing view to reference the newly chosen configuration.
Please let me know if this answered your question, or if I misunderstood.