Bob Stark wrote:
In Eudora, I solved this by un-checking the "Check email" on one of
the accounts, and just using the other (which receives all mail
regardless of which send-to domain address was used). Outlook does
not seem to have this option.

Tools-Send and Receive-send and Receive settings-Define send and receive
groups. select Edit, an uncheck the boxes under Account Options for the
accounts you don't wish to send and/or receive through.