It's by all means not extensible, since it is issued only once. However, the good news is that it's transferable.
I went through this process in April. My former passport was invalidated by my country and replaced with new (EU-compliant) passport. I had to transfer my entry visa (Multiple TRV), my study permit, and my postgraduate work permit. The reason for transferring the latter two is because the number of the old passport is printed on them. However, the Canadian consulate agent informed me that you may ask for a reprint of the PG work permit and the study permit OR you may keep the current ones (and the old passport for demonstration purposes). I exited Canada for a conference with the new passport and when I re-entered, the BSCA agent at YVR didn't even say anything about my study permit with the old passport number vs my new passport. I asked her whether it can pose a problem; she called her supervisor, who said that for as long as your TRV is valid and your permits are not expired, we don't care, given that the UCI/Client ID is the same and printed on them nonetheless...
Thus, ask for a re-print of your permit if you don't want to risk keeping the same.
