144 TWOV in China

Many articles on the 144 TWOV for China Cities. I am curious if it can be use twice? Example:
USA-Shanghai-Hong Kong, stay in Hong Kong for a week, then Hong Kong-Guangzhou-Taipei. Just planning for 2018, I am not able to obtain tourist L type due to born in Shanghai in 1946 and move to Hong Kong in 1950 then in 1966, immigrate to USA. I have no documents for both China and Hong Kong per the China Tourist L type requirement. Thank you.