Is it common/reasonable to build and manage a stack for each client?

I am trying to design a service that will sync with various clients databases and then serve that data to users. It is all time sensitive data, so it needs to sync very quickly and users will expect requests to be fast. At first I was naively thinking that I would spin up a server and database for each client. This would work well for 5-10 clients. Then I realized this won't work so well when we have 1000, but I am not sure.

Is is absurd to build, manage, and maintain a stack (DB, API, workers, etc.) for each client? Is that typically or ever done?