Yes, but you have to buy a Flexible 2-Day Pass. With this pass, you get to freely choose any 2 days you want to use Taiwan High Speed Rail (THSR) trains within a 7-day period. 

You also get this flexibility when you purchase a 5-Day Standard Joint Pass or 5-Day Express Pass. So in addition to using the Taiwan Railways Administration (TRA) trains for 5 days straight, you also get to freely choose any 2 days within the 5 days you want to use THSR trains.

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