Regulations Governing Visiting, Residency, and Permanent Residency of Aliens Article 11

Any foreign national studying in Taiwan may, after graduation, apply for an extension of residency with the NIA before his/her duration of residency expires. His/Her spouse, any of his/her children below the age of 18 or any of his/her children aged 18 or older who is unable to support himself/herself due to physical/mental disability may, if originally permitted for residency, also apply for such extension.The Alien Resident Certificate of any applicant whose application for an extension of residency under the preceding paragraph has been approved shall be extended for one year from the day following the date of expiration of the original duration of residency. Before the extension expires, he/she may apply for another extension if necessary, with the total extension of residency not exceeding two years.
中文原文 外國人停留居留及永久居留辦法第11條
來臺就學之外國人畢業後,於居留期限屆滿前,本人、其原經許可居留之配偶、未滿十八歲子女及年滿十八歲因身心障礙無法自理生活之子女,得向移民署申請延期居留。
依前項規定申請延期居留經許可者,其外僑居留證之有效期間自原居留期限屆滿之翌日起延期一年;延期屆滿前,有必要者,得再申請延期居留一次,總延期居留期間最長為二年。

English translation for reference only; the Chinese text prevails. Not legal advice.