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According to the [Republic of China National Immigration Agency, your 30-day single-entry visa would not allow such a request, as you must have a 60-day visitor visa without a stamp of no-extension.
Visitor Visa holders who are permitted to stay in Taiwan for sixty or ninety days and whose visas bear no such remark as "no extension will be granted" may apply at local service centers of the National Immigration Agency for a maximum of 120 or 90 days of extensions.
The ROC multiple entry visitorβs visa, usually valid for five years, allows multiple entries for stays of up to 60 days, although one 60-day extension may be granted by the National Immigration Agency, for a total of 180 days. For that, the place to start is at the ROC Consulate in Mexico.