What certificate is needed for one domain and different subdomains on different servers?

Question

Domain name market

There is a certain service that is provided to different clients. The service has a single
domain, but each client works with its own subdomains. All this works on different physical servers with several clients per server.
Is it possible to buy a single SSL certificate for this mechanism? Or do I need to get a separate wildcard SSL certificate for each server?
I specify: a different key is generated on different servers. Alexey suggested copying the key on different servers so that one certificate can be used. Has anyone tried this?

Answer 1

One Wildcard SSL certificate for *.вашдомен.rudomains.
UPD. And the same private key of the certificate on all servers.