To stay longer as a temporary resident you have to apply before your current status runs out, and you have to have kept every condition placed on your entry. If you still meet the same test that got you the visa, the officer must extend you. Applying late is not a small problem, it drops you into the restoration rules instead.
(1)A foreign national may apply for an extension of their authorization to remain in Canada as a temporary resident if (a)the application is made by the end of the period authorized for their stay; and (b)they have complied with all conditions imposed on their entry into Canada.
(2)An officer shall extend the foreign national’s authorization to remain in Canada as a temporary resident if, following an examination, it is established that the foreign national continues to meet the requirements of section 179.