Hi Paddy,
For the time being we can easily upload multiple files to a SharePoint Online library. About programmatically sending one file to multiple SharePoint Online sites, I suggest you visit the TechNet forum or the MSDN forum for assistance. The two forums are staffed with technical support engineers and Microsoft partners who can provide technical expertise to resolve the issue.
Meanwhile, you may refer to the community members in this forum who have the experience to provide the suggestions.
Thanks,
Cherry Wang