That's not multi-master in the typical sense, it's sharding, and done correctly, you shouldn't have any write conflicts because each shard should be strongly consistent within itself.

Typically a strongly consistent (CP) system works by having a single elected master where writes are only ack'd when they're written to the majority of the cluster. The downside of this system is you need majority of the cluster working and up-to-date and the performance impact of doing this.

A multi-master system is generally ( AP ) allows writes to any master node, but has some consensus algorithm where it picks and chooses winners based on conflicting writes. It should be faster and more available at the cost of potentially lost data.

There are some systems that claim to beat CAP but they typically have caveats and assurances that are required. After-all, if you ack a write, and then that node blows up, how will it ever sync?