This may be a Visual Studio question more than a nopCommerce question.
I made a copy of our solution on my hard drive so I could experiment with something. The paths are as follows:
Original C:\Source\Repos\NopCommerceProject
Copy C:\Source\Repos\NopCommerceProjectCopy
I have some breakpoints in a class in a plugin. When I debug the solution from NopCommerceProjectCopy, the breakpoints are hit in the equivalent file in NopCommerceProject. For example, I'm running NopCommerceProjectCopy, but I'm being shown breakpoints in NopCommerceProject\Plugins\Plugin.Name\SomeClass.cs.
I just tried your idea. While they're both running simultaneously, I get an Entity Framework error on one about an open data reader that must be closed before another can be opened. The connection string in each dataSettings.json points to a different database.