SINGAPORE - SHANGHAI-TAIWAN- SHANGHAI - SINGAPORE -Route

Good homework Gavin :)

Yes, both of your itineraries are eligible for 144 hours visa free transit in the wider Shanghai area that comprises Shanghai, Zhejiang and Jiangsu provinces. Also, there is no limit of how many times you can use 144 hours visa free transit within one particular time frame or in other words, you can have them without the limit in number.

Please, just have in mind that your flights do not have any additional landing within mainland China beside those in Shanghai.

Borut, Thanks for your kindly answer and advise.
If only one ticket is SINGAPORE-SHANGHAI-TAIWAN-SHANGHAI-SINGAPORE route, is it eligible for the double 144 hrs free transit in Shanghai? if yes, I don't need to book the separated ticket.
Thanks

That is correct. You can buy you entire itinerary on a single ticket if you want. The type of your ticket is not important. The only important detail is that the immediate points before and after your mainland Chinese destination are outside the mainland China area and that condition is satisfied twice within your itinerary.

Perfect and thank you!