The error page on any template 404 utilises the Joomla core so would need to extend the Joomla core functionality and install a new component
I'm not 100% what is on the Joomla Extensions directory - I do know sh404sef offers these features but for the 404 part of the system to work it does require the seo extension options to be enabled
The extension generates a list of similar urls from its database tables and displays them on its own generated error page (not a template error page)
Inside the admin it will track all 404s and offers re-direct options to re-direct them
This extension is quite complex to use and is a commercial one e.g. requires a purchase
To do this via any template is not possible
Regards,
Paul