According to your plan, you'll enter Canada for an exchange program, and do not require a visa but can remain in Canada for up to a 6-month period. This suggests that you are a visa-free national and, were you to apply for a study visa for a short exchange program, you might be advised that you don't require one, as the exchange is for only 4 months.
Rather, once you are in Canada, consider applying for an extension, and doing so before the end of your authorized stay.
Extend your stay in Canada as a visitor
You should apply 30 days before your status expires to:
- extend your visitor, student or work status,
- change your permit type (for example, from a study permit to a work permit) or
- change your permit condition(s) (for example, if you are studying and you want to change schools, or if you are working and you want to change jobs).
Find out how to extend your stay as a visitor.