2 different tickets - stopover for 144h possible

is it possible to have two different flight tickets - for example Airline A to/from Shanghai - and another ticket from Airline B from/to Shanghai to stay twice time in Shanghai to use the 144h visa?
i will fly from europe to Shanghai - stay 5 days in Shanghai - fly to taipei for 1 week - fly back to Shanghai for 5 days - then back to europe.