How did the western powers gain greater trading rights in china?

The first move the Western power made was done after the Opium war had ended and the was Treaty of Nanjing, the terms of this treaty was that China should open 5 of her ports. Second treaty still at Nanjing made China to keep her rights, lose just a little to other countries but allowed Christian teachers into China. Afterwards, some dramatic events occur such as the destruction of the Chinese Summer Place which had some amazing relics that are in British Museum up to this date