Just a head up, I believe the only reason OP could do this was his dual Canadian status. If he was a complete foreigner with no connections, I believe the banks would give him a hard time opening an account and I think (unless the rule changed) he'd need at least one Canadian to be on the board/ as a director and/or 25% share holder or something like that. He won't need a tax number for his partnership because the partners are taxed not the partnership and the bank will use his SIN number to report taxes.
OP did not mention in canada, the banks are mandated by law/policy of the government to provide all Canadians with a bank account so they cannot refuse Canadians (but can foreigners) so it will be piss easy for him to open an account.
Also just because the LP is not a "tax resident" of Canada doesn't mean it is not subject to taxation, specifically withholding taxes. If OP uses that Canadian company and does trades on Canadian stock exchange he is going to be made to pay a very high tax rate on whatever he earns.
I'd also caution the OP to seek legal advice and be extremely careful because he is skating on thin ice.
1. He owns a company in Canada
2. He is conducting business in Canada
3. He holds a bank account in Canada
4. He is going to be made to pay tax in Canada on whatever his business earns, including its foreign income unless subject to a tax agreement
5. CRA might come a few years later and say this "Belgian" non-resident guy has a Canadian bank account, Canadian ID (passport, driver's license, healthcard, SIN), Canadian renter/tenant (after all he needed an address for the bank and his company right), owns a company in Canada that SHOULD be paying taxes here. You are at an extremely high risk of being classified as a Canadian "factual resident".
I just have 2 question for you, when did you notify the CRA you emigrated from Canada and when did you file your departure tax forms?
You are indeed raising some valid points. Indeed I cannot not provide legal advice to others, but I am simply sharing my experience. I would like to clarify a couple of things though:
1. I left Canada back in the late 90s and while I regularly travel back and forth (usually a few times per year for a week at a go), other than a Canadian passport, I do not hold any other Canadian documents, nor do I own any property there. I do have family ties, but my immediate family (wife/kids are Belgian)
2. I am not conducting any business in Canada - I just have a registered LP in Canada. The business activities is conducted outside of Canadian borders and it does not trade in any Canadian listed securities
3. I don't hold any Canadian Bank Account, but the bank account is fully under the name of the LP
4. I don't have any OHIP Card anymore and my SIN card has not been used in over 20 years. I don't even have any Canadian credit cards.
As for the ease of opening a bank account due to local connections - I don't know. I just went into a random BMO branch in the outskirts of Toronto (where there is a high immigrant population) and opened an account using my Belgian papers, but not knowing anybody working in that branch. I think the branch was familiar in opening accounts for non-residents/foreigners and thus I found no issues in opening my LP account.
Although my Canadian passport was never used during this whole set up I cannot say for sure whether one could do this entirely with a foreign passport. I personally believe it is possible, as I only used my Belgian ID at the bank, but I cannot say for sure that this could work for everybody.
Hope this clarifies!