ArcGIS Enterprise is a complete platform for mapping and analysis that allows organizations to easily manage their location-enabled data and host a browser-based GIS using their own IT infrastructure.
If you do your online mapping using ArcGIS Enterprise instead of ArcGIS Online, you can now use Story Map Cascade, which is included in ArcGIS Enterprise 10.5.1 Portal.
It is also easier to use My Stories (our management and issue checking tool for story maps) within your Enterprise portal via a new item that is provided in the system. For example, your admin can add that item into the featured content group on the home page of your Enterprise portal so that all the users of your portal can access it.
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In ArcGIS Enterprise 10.5.1 Portal there's now a standard item for My Stories (the first item you see below), which makes it easier to access the My Stories functionality.