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That's a typical error many support centers commit when setting up a live chat in addition to their phone hotline. When one support agent does not know what the other one is doing, you are bound to drive the customer crazy. The best approach to this is just building up a very ressourceful internal communication network, optionally in a cloud, that allows everybody to benefit from the data, knowledge and information available to their co-workers. I've had that set up once and it was a huge investment, but even in the short run it proved to be the right decision. It did flatten internal hierarchies, though, so you have to be aware of that.