The Taiwan Ministry of the Interior amended its rules on extensions of residence on 5 December 2018 with immediate effect.
Under the new rules, most holders of an Alien Resident Permit (“ARC”) for the purpose of professional work in Taiwan can extend their residence for up to one year after his or her ARC expires. Regulations Governing Visiting, Residency, and Permanent Residency of Aliens (the “Regulations” §22). Under the old rules, the Ministry permitted only one extension of up to six months.
The new rules also permit a foreign graduate of a Taiwanese university to extend his or her residence for up to one year following graduation. Regulations §22-1. Overseas Chinese graduates are also eligible for similar extensions of residence after graduation. Regulations Governing Residence and Permanent Residence of Nationals without Household Registration in Taiwan §18(3).[1]
Classes of Foreign Professionals Eligible For Extensions
Eligible classes of foreign professionals include:

1. Professionals and technical workers (Class A),
2. Directors and Officers of foreign-invested businesses (Class B),
3. Language teachers at public and private schools and universities (Class C),
4. Teachers at cram (buxiban) schools (Class D),
5. Coaches and athletes (Class E),
6. Artists (Class F) and missionaries, and
7. Crew members of merchant vessels.

Others eligible for the extensions include consultants and researchers at government agencies, research institutes, certain types of visiting academics, foreign investors, and persons specially approved for residence by the Ministry of Foreign Affairs.
A professional ARC holder can also apply on behalf of immediate family members (spouse and minor children) for extensions of residence.
How to Apply
An eligible ARC holder must apply for an initial extension of six months before his or her original ARC expires. A second extension of up to six months can be applied for before the initial extension expires. Applications may be filed at a National Immigration Agency service center no earlier than 30 days before expiration. Regulations §8(1).
Special Rules for Adult Children of Foreign Residents
The new rules continue to permit the adult children of foreign residents who grew up in Taiwan to apply for two three-year extensions of residency if they meet certain minimum residency requirements as minors and apply during the 30 days before expiration of a current ARC. Regulations §8(2).
Since February 2018, adult children of permanent foreign professional are also eligible to apply for work permits as adults if they meet certain minimum residency requirements as minors. Act for the Recruitment and Employment of Foreign Professionals §17. These work permits can be applied for when the eligible child turns 20.
For questions about immigration matters in Taiwan please contact Michael Fahey at mfahey@winklerpartners.com and Christine Chen at cchen@winklerpartners.com.

[1] 臺灣地區無戶籍國民申請入國居留定居許可辦法