It's a C. texensis hybrid, perhaps Duchess of Albany. It doesn't look quite dark enough to be Princess Diana.

If you go to the link below, the fifth category is a drop-down menu for Group. Choose texensis and it will give you a list of ones in this group having a general shape like yours. Click on the names and you will get photos and other info about each kind. Keep in mind that some colors are difficult to photograph accurately, but this may give you some other possibilities. Not all types will be available commercially in the US.

Alternatively, clematis are fairly easy to reproduce with layering, and that would give you clones of your current plant.

Here is a link that might be useful: Clematis on the Web search page

I think it's one of the texensis varieties like Duchess of Albany or Princess Diana, and although I've never moved one of them, I have moved enough other clems that I'm pretty sure you'll be OK.

THank! Looking forward to layer it and distribute among my garden!