What you mentioned is the only thing I've been able to think of so far as well. I haven't gone down that road yet because dividing the database would make things more complicated. The data also will require periodic (at least hourly) "global summary inquiries" -- and maybe updates across all user accounts as well.
I was wondering if it were possible to do this against one database instance. I just don't know the upper limit of the software component parts. I'm not aware of any definitive source that spells out what the upper capabilities of the software components happens to be. I suppose a lot depends on the specifics of implementation. But I don't know of any specific implementation of any sort at this scale that's available with reliable and proven benchmarks.
I **very much** appreciate your input. Please share whatever comes to mind. Basically, think of a central system with the same type of data for each user. It's just that the user's "set of numbers" is constantly changing and that they all need to access it and or update it at the same time at several points throughout the day.