Is there a VOIP system I can use for incoming calls that has a sophisocated programmable IVR?

I would like the caller to have several options, some that give further menu options, some options will play messages, and other options will connect the caller to a live operator. I can record the prompts myself. The calls should be answered on a VOIP phone.
It must have an IVR to answer common questions automatically and be able to handle multiple simultaneous calls. Probably 3 callers at a time will suffice.

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