I've considered doing this for some time now. Do you have any sort of link between the two accounts? Maybe not directly, but e.g. are both connected to the same brokerage or anything? Is one online-only or do both have physical locations somewhere?
One is online only (the one I use the most), the other one is a completely different bank with very different objectives and clients plus physical offices everywhere.
Each account can send money to the other via wiring, but that's it.
Saved my ass several times already when I lost my credit cards or other unpleasant situations.
