I think it all depends on what platform it's running on - much more likely to be a limitation of the operating system than SU itself.
I run it under Wine on xubuntu 14.4, mostly. It thinks it's running under Windows 7.
Xubuntu/wine allows me to start at least two instances of SU, but I think neither is 'aware' of the other, as they'll be run as if on separate Windows machines.
I can cut+paste things like strings (numbers or text), as that is going through the clipboard of xubuntu and being re-translated (because that's simple and easy to do). I haven't attempted more complex objects, but would expect that to fail.
I very much doubt it would work in 'proper' Windows (it might though), and if it does, I'd expect problems with file locking if you tried to open the same source file in both. SU isn't intended to be multi-user, as far as I can see, without making use of the 'cloud' SU Warehouse, which does allow you to share 'privately' (if you see what I mean).
If I understand what you're trying to do, you have a second, new version of your model, I assume as a separate file. If anything's going to work under native Windows, that will.
E.
PS: Someone who actually knows will probably be along in a minute or two...