Copying a model
You can definitely copy a models data via a process into a new model if the structure of the new model already exists. But this must be predefined and currently there isn't any functionaility to copy a whole model via an automated process into a new model. However you can create a whole copy of a model using the 'Versions' functionality which will allow you create another version of the model but this will exist in the current model as a dimension.
I hope this helps to explain what is possible and if you'd like to some further explanation on how to create a copy of the model using the 'Version' functionality please do let me know and i'll be happy to guide you.