It's possible but I don't know of anything open source that exists yet. The stack I'm working on deals with the underlying issues you describe, including storage and identity/connectivity (which is the basis of the social network aspect you mention) [1]. I commented a few days ago on how such a system might work for the example of photos [2].

[1] http://nymote.org/ (which uses MirageOS unikernels http://mirage.io)

[2] https://news.ycombinator.com/item?id=9026778