If our game is successful we could have upwards to 10,000 requests a second.
That's on the same magnitude as the average number of Google searches globally.
Your title mentioned it as a login server. Consider the top-tier Facebook games are just barely hitting 7M Daily users, which averages out to 80 logins per second.
It is highly unlikely you will hit 10,000 login requests per second, EVER.
If instead that is your main game, then supporting 10K simultaneous requests is going to probably have bandwidth --- not server capacity --- as your biggest problem. You'll be looking at multiple fiber connections to handle it.
A well-designed system will accept an arbitrary number of computers. A master system allows an arbitrary number of worker machines that handle the connections and such. A good design allows them to be added and removed from service at any time, so you can scale up your number of servers with ease.