Turkey, only a tiny part of which is geographically in Europe, is a candidate (though talks are suspended in practice until, at least, Erdogan is out of power), and Cyprus is geographically in Asia/Middle East, not Europe. The rules could certainly be loosened further with agreement.
But also, yes, Canada probably does not want to be a full member, at least in the near-term; they want some sort of alignment not amounting to full membership. I wouldn't be totally amazed if we look back on this as the start of the (long-suggested) two speed EU system.
Good point regarding Cyprus but considering the political and social situation in Europe I think that any loosening of the rules is a non-starter.