There might be a way by making multiple passes thru your die cutting machine and strategically placing your cutting plates so that the first pass cuts part of the die and then you could readjust your paper that is partially cut and make a second pass through the machine to complete the cut on the 'extended' part of your card. You might have to place a paper shim or something at the end of your cutting plate as protection so that the end of the cutting plate doesn't make a 'dent' in your cardstock when you are only cutting part of the card.
I hope this makes sense.
And you can always call or email sizzix here:
https://www.sizzix.com/contact
HTH.