KYC for corporate accounts with complex ownership structures

I'm looking into opening a corporate account for a new venture, but the ownership structure involves a few layers of holding companies across different jurisdictions. I've heard some banks can be particularly stringent with KYC in these situations. What kind of lead times or additional documentation should I expect, and are there particular jurisdictions that tend to cause more headaches than others when the ultimate beneficial owner (UBO) isn't immediately obvious?