I would really step back from the 3 current workspaces and ask myself do they server a common purpose? I would also ask if there is a common culture in those spaces. I have encountered organisatons that have more than one collaboration space, often departmentally siloed. To assist I have looked at the processes and business functions that each workspace supports and have asked myself if it is possible that they can collaborate. A workspace designed to support an engineering design team is unlikely to have the same culture and approach as a workspace delivering collaboration services to the financial team or the HR team.
I have had success addressing disparate workstreams using a Business Process Re-engineering (BPR) approach. I have increased the inter-operability of disparate workspaces by re-engineering the process they support.
By doing this the workspace becomes more "inviting" becasue the value proposition offered is more tangible.