As per my experience in Bangladesh that USA always issue 5 years multiple visa and passport in BD is valid maximum 5 years . Even though passport is expired but visa is valid and good to use subject to you get another new valid passport and travel with both. In Bangladesh I used to carry 6 books of old passport along with one valid . You don’t need to transfer or apply for new visa.
This is true once your passport has a valid vis even if it is expired you can brink it along with a valid pssport.
however in our cases canada does not allow you to have Two RTD's at the same time so they will not issue a new one until they have the old one back. so you kinda have no other choise but to get a new US visa at which point the VO will cancel the old visa and provide a new one upon approval and most times you are approved once you tell them the reason and they see that you already have a ten year validity in the old one.
Good Luck.