What you could do is use Twilio or other similar services and unconditionally forward the number of Twilio. Then, in Twilio, use scripts to handle the verification steps of incoming calls. Once the verification is done, forward the call to a direct number in queue x and let the call center take over from there. The "x" queue must not be on the list of queues / groups of the automatic receptionist and must have a large number so that it can not be called by random people. Basically you need 2 groups for each group in which you want to do these checks.
I do not think they have an option to add logic to their systems beyond them by doing webhooks and using their API to get information. The IVR options sounded good, but it seemed they were only obtained.