بسم الله الرحمن الرحيم
No, you cannot deduct the additional amount from your zakah money and thus your zakah will not be paid. For the payment of zakah it is mandatory that the intention of zakah is made while giving it to the poor person. Yes, you can give your zakah money to that poor person and he will become its owner and thereafter you may demand your debt from him.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.