More than 30 days gap between my visa expiry and new course

My student visa expires on 30th of Nov and my new course starts mid of Jan next year.

Although I am aware that in the instance where my new course starts 30 days after the expiry of my current student visa, I will have to go back home and get my visa issued from there but clearly I don't want to do that.

But I think I have a tweak. I have an exam remaining to do (from my current course) towards the end of December. For which the result will come out mid of January.

Can someone guide me if I have any other option than applying for visa twice in quick succession (i.e. once for my current course and then for my new course)?

Thanks.