Add each reference and change their default alias. If you find the assembly under the references node and view its properties you'll see it has an alias of "global". Change that to "newDll" for your new assembly and "oldDll" for your old one. You can now explicitly refer to each assembly via;
oldDll::MyNameSpace.MyClass
newDll::MyNameSpace.MyClass
Or use aliasing in the using list at the top of the page
using OldProduct = oldDll::MyNameSpace.Product;
using NewProduct = newDll::MyNameSpace.Product;
then in your code
OldProduct p = new OldProduct
If you want to simply have our code use different versions of the assembly then update the web.config\app.config file appropriately.