Single Entry to Multiple entry - Possible?

Hi I havnt been able to find any info about this:
Im in Taiwan with a 60-day single entry visitor visa that is soon to be expired and im going on a vacation and visa run to HK. Does anyone know if i can apply for a 60-day multiple entry visitor visa even though the original visa i have from my home country is a single entry??? Im not here to work or study just to travel and visit my friends that live here so i dont have any special documents, will this matter???

Thanks in advance for any info!!