Mercer published this definition and contrast of Co-sourcing versus Outsourcing on their website. I must beg to differ. While in general they are correct, the term co-sourcing has been around for a long time - probably originally coined by Mercer.
These days if you are a large employer and outsourcing part of your HR delivery, you should be approaching that outsourcing partnership with the desire to improve service delivery by some measure as opposed to simply reducing costs. This should be the objective regardless of how transactional or administrative the outsourced transaction is.
Co-sourcing is simply another buzz word that was created to help outsourcing consumers understand the impact of partnering with their outsourcing vendor. The term has outlived it's usefulness. I've heard variations from multiple vendors now including intersourcing. All of this is simply an attempt to explain the vendor relationship and allow it to evolve into a strategic partnership where both parties are trying to add value to the client organization.