How to add a second checking account within Quickbooks without loosing history

We have an existing Quickbooks account with a history and currently process on-line banking using Direct Connect.  We want to change banks which require a web connect through Intuit/bill which uses Fiserve to pay bills on-line.  Is there a way that we can migrate to this new service and just append the existing ledger/history that already exists.  We would like to keep both vendors(Banks) to maintain history.  Everyone is warning us that if we deactivate the old bank we will the history that already exists.  We seem to be able to pay the bills on-line, but when we receive or import the transactions from the new account we are getting a warning that it will create a new set of books or ledger.  Not sure of the exact wording because I did not personally see the error but appears that we would end up with two sets of books and the customer only wants to keep a single set.

First is this possible and if so can someone point me in the right direction.