A single deployment server (that is not also an indexer or a search head) can handle up to 500 clients. For more clients it depends of the periodicity, and the size of the bundles to deploy.
(Personally I never saw a server able to handle more than 800 without stopping serving )
The solution is to have several instances of deployment-servers ( on the same box or others), and always use dedicated deployment servers.
In my current project, the deployment server is able to handle 5000+ clients in AWS .. But we face lot of slowness while adding new server class, clients etc. Otherwise, its fine. We are planning to deploy more deployment servers to handle 1000 clients per Deployment server.
In the enterprise infra, the deployment server is able to handle ~800 clients without any issues and no slowness aswell.
CPU load is always < 1 .. And the poll interval set to 300 seconds