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No. It is not permissible because if you are a resident in Canada you cannot have a driver's license from somewhere outside of Canada that you can use. If you are a visitor to Canada you could use the US driver's license. But, as soon as you took up residency in Canada you would have to destroy that license. In fact it is even an offence to have driver's licenses from more than one jurisdiction. So this is not a possible solution at all.