See my comments at
The technical part is easy; the trick is how to not annoy the customer. If you have plenty of people to field calls, offer a callback (which will happen immediately), put the customer in the queue and with luck it will be answered immediately or at least very quickly.
OTOH, if the problem is that four of the five channels are customers waiting on hold for a single overloaded agent, you need to think about how to solve this without too many customers fleeing to competitors. Possibilities include taking a message, suggesting hours when you’re not so busy, suggesting alternative communication (self-service on website or app, ticket system, chat, email), hiring more agents, having existing staff take customer calls when the queue is full, etc.
Feasible to increase channels? Which country? I’m guessing UK because you said DDI. For example, Voxbeam charges $6.60/mo./channel; what are you paying now? Or, maybe paying per-minute would work better. For example, AnveoDirect charges $0.004/minute. I don’t know whether these are competitive prices.