maybe google some banks as each bank has different requirements for non residents, such as TD or RBC or even HSBC. Most arrangements are for new immigrants but some have non resident capability with restrictions.
Banks really don't care what is your immigration status to open an account, the problem is that one of the IDs has to be a photo ID issued by a Canadian institution.
you can
your first ID is your passport
the second is a another perssen who have un account in the same bank , they put his information with your account