You'll have to open a bank account in your name somewhere, then, most banks will allow you to open a new one via their internet banking portal.
TD Canada Trust, Scotia, CIBC, RBC... they will all allow it.
As for unlimited, there is no such thing. Everytime you open a bank account it will get listed either via the Chex system, or even on your credit report. While having 50 bank accounts does not affect a credit score, opening many and closing many could look suspicious or look like money laundering practices...
Some people have been refused service in a bank after a while because they were opening too many. If you are semi-honest and explain why you need them, some banks will be more comprehensive than others.
Good luck!
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