Obtaining new double entry visa immediately after one has been used

My boyfriend and I were both granted double entry visas for China even though we applied for multiple entry visas. We were told we couldn't get multiple entries because we applied from outside our own countries (New Zealand and Australia). We plan on entering China from South Korea, exiting to Taiwan then re-entering China, thus using our double entry visas. However, we want to go to Hong Kong then re-enter China to visit Mongolia, so we would like to know if it easy enough to apply for another double entry visa while we're in Hong Kong.