I'm working with a system where I would like to use the dateext function of logrotate (or some other way) to add the date to a logfile when it is rotated. However in this system it is important that no logging is missing and dateext will overwrite any existing files (which will happen if logrotate is called twice on a day).

Is there a reliable way to prevent dateext to overwrite existing files, but instead make another file?. It is acceptable that either no rotate happens or a file is created with a less predictable name (date with an extra number, or the time or something).