We have a few people that oversee multiple sites. I have all certificates scanned in a certificates folder I can access from any site. Originals with individual names are kept by the individual at whatever site they want. I've never been asked to see the original, the pdf scans have always been accepted.
We have 4 sites and I can access the pest control information for all sites via the pest control companies website, all their visits are logged electronically. They have their certifications and licenses posted that we can pull up for auditors. Physical log books are kept on-site at each location, but the company allows us to report things via QR code directly to their site (anyone can do it without a login as the QR code is linked specifically by site - these are posted in a number of places around the warehouse) which allows us to attach pictures and the PCO is aware before arriving and can prepare as needed. We also call if we think it requires an immediate visit.