Not that I’m aware of - at least not ways that are supported by Oracle. Even for 11.5.10, there will be times when the system is down (I consider maintenance mode down as it means the users can’t access the system). The newer releases provide ways to reduce the down time, such as creating staging areas of the middle tiers that can be pre-patched and then cloned over. Even still, there are always dependencies between the file system objects and the database objects, so you will have downtime when applying major patches to the database. Of course, this is just for applications patches. Technology stack patchs (database upgrades, apache, iAs, etc.) will require downtime as well.
We sometimes merge patches to reduce the down time when applying several patches to an environment at the same time.
I always recommend going through a few interations of major patch(es) in a full clone of your production environment before moving into production. This allows you to identify any issues and correct them, and well as providing you with an estimate of the outage required when migrating to production.
Regards,
Michael