Visa Extension Question

[Cal23]

Hello,
I am a US resident who has been living in Canada for the past 5+ months on a temporary resident visa. My visa is set to expire mid-June. I was originally planning on just leaving Canada at the end of my visa but circumstances have changed and I need to stay. I know that you're supposed to apply for a visa extension 30 days before your visa expires. However, is it possible to still get an extension if you've passed those 30 days? I'd assume that you would need to send the application via express mail or 1-day courier. Thank you in advance for any responses.