Hello Yigal.
We don't currently offer this functionality, unfortunately. You can solve for the optimal route and then use barriers to block key parts of that route and solve a second time to get an alternative that avoids the barriers, but this tends to be rather imperfect and hard to do.
If this functionality is important to you, please repost this to the ArcGIS Ideas site as an enhancement request: https://community.esri.com/t5/arcgis-network-analyst-ideas/idb-p/arcgis-network-analyst-ideas Enhancement requests posted in ArcGIS Ideas are tracked differently on our end than questions here, and it also gives other users the option to upvote the idea. Alternatively, you can log your enhancement request with Esri Support or Support for the distributor in your country.
When you post your idea or call Support, please add as much detail about your use case as you can. Explain why you need alternate routes, what the goal of your analysis is, etc.
