My SBM version is 11.8.

I would suspect that the entries in the ts_notificationevents table that represent scheduled reports got duplicated.  You can view your scheduled reports in your user profile and verify that you only have the report scheduled once.  Perhaps, your scheduled report entries in the ts_notificationevents some how got duplicated.

David's answer is most likely correct for the original issue of getting duplicates (2 copies). That idea could be the same why you get 4 copies now. I'm not sure.

I have seen another rare situation that causes duplicates. In this situation, "duplicates" means that you get 4 copies now instead of 2. For example, if the Test server is pointing to the production database by mistake, the Test NS could be sending a copy as well as the Prod NS. Each would send the 2 notifications, giving a total of 4. To check this issue, look in Configurator on the BOTH the Component view and the Database view on BOTH test and prod. Just make sure Test is only pointing to Test and Prod is only pointing to Prod. 

See if that helps.

I did check, and it's only scheduled once.  There are 4 templates in the Advanced drop-down, with the default one at the top of the list; I don't know whether that means 4 versions are being scheduled or just the one that appears at the top of the list.

I will check that.  We also have a Dev server, but only the Test server was refreshed from Prod, and I may have forgotten to delete the events table.  Still, the test server Configurator notification is set to Test, so it doesn't send emails.

I'm checking with our DBA on the fact that although the test server service name (includes "test") for the set of database files and for the Repository (includes "prod") are correct, respectively, the Host names are the same.

Toad shows no data in the test database TS_NotificationEvents table.

If the scheduled report entries in the table were duplicated, and then quadrupled, how could that be fixed?  There are a couple of reports scheduled daily, and many weekly, and many monthly.  If I were to empty the table, would it populate the next day automatically?

I'm thinking that since we don't have escalations, if I delete the table after work hours, it would work nicely starting the next day.

DBA confirms the Host is correct.  Still no cause discovered.

From looking at the templates in the App Admin, I concluded that only one template is in use for any scheduled report.  Only two templates show data in the Usage column, which contains too much data to display more than a couple of reports.  I wonder if there's some way of viewing all the reports that use a template.