Hi Sonja,
The short answer is yes, you can make a copy.
But the longer answer depends on where you are building the storymap.
A couple of quick questions to help things along.
Are you building the storymap in Portal, Web App Builder (Developer) or ArcGIS Online?
And have you heard of ArcGIS Online Assistant?
I think that AGO Assistant will be your answer. It is fairly simple to use the online version, the developer edition on GitHub takes a bit to set up, but is just the same as the online version.
If you are building it in a Portal that is on the Web or on ArcGIS online, then use the link above to AGO Assistant.
If your Portal or Web App Builder (Developer) is not accessible to the Web then you may have to install AGO Assistant in your environment.
<Edit> Web Apps that are developed in Web App Builder Dev edition can only really be copied once they have been hosted on a Portal.
This link should help if you need to install AGO assistant:
GitHub - Esri/ago-assistant: A swiss army knife for your ArcGIS Online and Portal for ArcGIS account...
Hope this helps,
Michael
