Increasing the number of shards is similar to changing the backend infrastructure, but simpler. Downtime obviously isn't acceptable, so when switching from one system to the next, we have a period during which we write to both so that it is safe to read from either one. Other schemes could be used for resharding, but this is simple enough and also works for other changes, and in practice we've changed the schema more often than the number of shards.

Also, keep in mind that it is ok to have more shards than you really need (multiple shards can run on the same machine, for example), so resharding needn't be a common operation.