Taiwan endorsement issue, entered Taiwan many times

It is theoretically possible to use a passport and Taiwan entry permit to exit Beijing and enter Taiwan for the first time, use a passport and Taiwan entry permit to exit Taiwan for the first time, and then use a passport and Taiwan entry permit to exit Singapore and enter Taiwan for the second time. It is recommended to confirm with a visa professional.

No, one-time endorsement is enough for entering Taiwan and stamping for exiting Taiwan.