Failing a mortgage stress test means that you will be ineligible for a mortgage at any federally-regulated lender. This includes all of the Big Banks in Canada, including RBC and TD.
If you have failed the mortgage stress test, or you are looking to avoid it, you may consider un-regulated lenders, such as private mortgage lenders. Private lenders are not required to conduct a stress test and they are generally more flexible in their lending requirements, such as if you have a bad credit score or if you are self-employed. However, private mortgages come with much higher mortgage rates, even in excess of 10%.
Switching lenders or refinancing your mortgage also means that you will have to undergo another mortgage stress test. Staying at the same lender means that you can avoid the stress test, but it might mean that you can miss out on better mortgage rate offers at other lenders.