However, supervisa has to be applied from home country!! that's what my presumption is. If your father has plans of visiting home country then super visa could be applied. If no, then extension seems to be the right option. I don't know how they would assess super visa application when the person is already in Canada.I
I had similar case:
My Father supervisa was expiring on 31st Jan, So I called CIC in Oct to know my options. they told me to apply for extension.I applied on 8th Oct , on 7th feb I got my approval for extension. . But, I called CIC today, and they said, this is just an extension for stay. He can live here till 31/12/2020. but its not a multiple entry visa, So now I have to apply for supervisa again. agent said, yes, I can apply for supervisa at this moment