One place I worked at had 3 people also, but also supervisors, directors and managers.
Basically if the workers are bringing up good ideas that require group effort enough times, consider their experience and ask them if they would like to run with it? They might say yes. = 1 new supervisor.
Supervisors tend to be the official word on any matter not being handled by level 1. They would still be in customer service, just more like a lead position, helping others along where they vary.
When you have two leads, then one turns out to be your manager. Some people are great leads though, and not manager types. This may take a while. Also managers tend to be more strategic thinkers. If they see no reward for more responsibility, I can't see anyone sticking their neck out too far. This is known as The Sqeeze.
However, without the real experience of the call center behind them, the manager can't make the connections between other departments necessary to bridge together service offerings and reduce repetitive customer contact.