If you are changing to a different credit card account you don’t have to pay the duty more than once. When you are closing the account your card issuer will give you a letter of closure stating that you have paid your stamp duty for the year. If you give this letter to your new card issuer, you will not be charged stamp duty by them for that year. You can change account as often as you like during the year without paying extra duty, as long as you transfer a letter of closure between the card issuers each time.