One of the "more fundamental changes" to the switching process would be the introduction of account number portability (ANP), which would "mean that a customer would effectively take their account number (and maybe their sort code) with them when they switch banks".
"This could make the switching process easier from the customer’s point of view and could give customers more confidence that payments would not go astray," the watchdog said.
The CMA acknowledged that this would involve substantial changes to the payments systems used by banks - and revealed that the estimates of how much the ANP would cost "vary between £2bn and £10bn".
On that basis, the CMA said it would explore the role of its Open Banking programme first, although it added that the Payments Systems Regulator "might want to consider ANP at a future date".
A spokesman for the watchdog told City A.M. that it had decided the ANP solution was "not a relevant switch to make".
Another of the changes the watchdog is considering is to extend the current 36-month redirection period for switched accounts "so as to provide further assurance to customers that their payments will not go missing after they switch banks".