From what I was told via OL is that the Connect designer can only have one instance open at a given time on a single workstation. To copy from one template to another, start by exporting your scripts from the templates Scripts tab. After that you would copy all images and other resources from the template. Once that is out of the way go ahead and copy all the code for your templates div’s, tables etc from the Source tab and put the code into a text file. From there you can add all this back into a new\other template.
Another option you can use is to open the template file with your favourite ZIP software such as 7Zip. The file is merely a zip containing the template files including some not directly editable in Designer.
I would take this approach cautiously, for example by making a copy before unzipping and not using it to make changes to a template.