Is it possible to allow Private Number or Hidden Number calls past DND?

Background: My wife and I are foster parents, and our sponsoring agency uses its on-call phone system to call foster parents for emergency placements. The system has a single inbound number that forwards calls to the cell phone of the case worker who's on call that week, but for whatever reason* outbound calls placed from that case worker's cell come across with CID hidden. (I've seen both Private Number and Hidden Number, which I assume are carrier-specific variants.) *I'm aware of the personal privacy and work/life balance reasoning behind the decision. I just don't know why, instead of hiding the CID, they don't set the CID to the inbound number. Context: I've got a OnePlus 9 Pro 5G that was recently updated to Android 12. During the workday (8A-5P) I have Do Not Disturb enabled, with calls from Starred Contacts allowed. I also have the "2 calls within 15 minutes" rule enabled, but I don't know how that works with non-CID calls. Question: Is there any way to allow non-CID calls past the DND feature?