iOS 3rd-party mail app which allows connections to multiple ports at the same time
I do not know of a third party application. But besides a vpn, you could try going to settings>mail>your specific mail account. This may give you the option to change the incoming mail server, but it may not. But you can change the outgoing mail server by adding a entire new secondary server in case the first one doesn't work. You can look at the pictures attached.