Something which I've seen being used on PostgreSQL databases which could also be used on MongoDB with a little bit of work ... RabbitMQ is added in front of the database, any insert / update / delete that is done on the primary DB is thrown on a fanout exchange which fans it out to other databases where the same operation is then applied.
So if you have 3 queues to fanout to, any operation that is done on the primary database is replicated via RabbitMQ to 3 other databases without performance penalties. If you need to do maintenance on a database, simply switch to a backup copy of the DB, any updates you're missing will be queued on RabbitMQ and be applied as soon as the DB becomes available.
So this is effectively backup via replication.