It is a bit of a lame answer perhaps, but since the DXA team is building both the DXA Java and the DXA .NET web application, yes we have some experience with sharing a design. Also looking forward with DXA 2.0, we plan to add support for Client Side JavaScript frameworks through the Model Service.
But in general, it shouldn't be a very hard task to align all your web applications on a single design (the single HTML design for DXA was one of the easiest things to accomplish, aligning the architecture between Java and .NET was way more complex). Sure there is a difference in view technology etc, but if you use one HTML standard (DXA choose Twitter Bootstrap for the standarized grid in its HTML), then you can reuse that HTML over all your applications.
#update
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In general you should get rid of apps which need to add logic (as in code) around the HTML, and also you should try and steer away from changes in the HTML though using an HTML standard/framework. With proper semantic HTML, the only changes that you ever need to make for a changed design should be CSS (and possibly JavaScript). The CSS (and JS) you can distribute as part of a build/deploy process, without the need for the application itself to require changes.