For sure, but going to a new lender would require qualifying and we recently had problems trying to qualify to re-mortgage an existing property, none of the regular lenders would look at us.. too many properties, too complicated a structure, partners, etc.
We've been streamlining things to make it easier for lenders in the future, but we're not done that process yet.
I will definitely point out other banks' rates and they don't know my talk about leaving is a hollow threat, but ultimately it is hollow