I mean you can add a chain or other detachable strap if you don't mind the top handle on this in the way, but the attached strap that comes with won't crossbody.Here's a better picture that matches holiday123's comment and looks more like the strap drop listed on .com:
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I couldn't make it work because the clips on my chain were too small and made the bag hang funny. Using a larger strap or adding o-rings was just making it look wonky too. In the end I returned and purchased that snakeskin lunchbox so I would still have emerald in my collection. It's a gorgeous bag though if you like to shoulder carry.