You certainly can, it's almost certainly unnecessary though. SSH keys are not like passwords, compromise of a server with your pubkey in no way effects the security of your private key. Many people will post pubkeys online so they're easy to add to new servers.
I use a different keypair for every service, and for each device connecting to the service because keys are cheap and easy to manage. One advantage is that if one or more private keys is compromised or potentially compromised, you don't need to revoke and reissue all keys. Another, possibly more practical advantage is that I prefer to have a per-service persona that is not tied to other services. Shared public keys makes it easier to link together different accounts as belonging to the same person.
