Is it possible to use the visa-free stay twice within the same month?

Hi! I am planning to travel to Hong Kong, Macau and Taiwan with separate stopovers in Shanghai and Beijing. My route is going to be:
Copenhagen - Shanghai - Hong Kong - Macau - Taipei - Beijing - Copenhagen. As far as I understand, Macau, Hong Kong and Taiwan are considered to be third regions for transit purposes? Would it be possible for me to take advantage of the 72-hour visa-free stay in Shanghai on my way from Europe to Hong Kong and another 72-hour visa-free stay in Beijing on my way back from Taipei to Europe? It is around 3 weeks between Shanghai and Beijing. Thank you very much in advance!