Maintain uptime with Amazon Aurora during re-indexing?

When you run REINDEX VERBOSE INDEX <index-name>;., is it possible to do this on one AZ at a time, or some other way of maintaining up time throughout the process? Would you need a multi-master cluster for this to be possible?

This would suggest so:

With a multi-master cluster, your application can redirect write operations from the failed DB instance to any other DB instance in the cluster.

I wasn't sure by reading this maintenance doc.