Simply overwrite Backbone.sync
so that it sends messages down socket.io and tells the relevant backbonejs models on the server to alter state.
The interesting part of this solution is setting up the master-master relationship. You need to insure that for any client they can only "update" the state of models on the server that they have "ownership" of to avoid hackers and server-side state corruption.
So for each client they have a set M where that client is the master of all models in M and has a set S where that client has slaves of all the models in S.
It can only force updating on the server of models in M and only one client should have a particular model in M (or you need to implement a solid locking / merging implementation).
Whenever a model on the server is updated you simply push out to any client who has that model in S. (and push to any client who has that model in M if the model is in M for multiple clients).
A lot of thought needs to go into control / permissions and ownership that is normally handled by the MVC controller once a client POST/PUT/DELETE some data.