Let's make this simple. I have a website hosted on a single dedicated server (LAMP).
All static content are alraedy on an external CDN.

PHP pages aren't a problem because they take pretty low time to load (0.05).

What is a good strategy if i see my dedicated server can't handle more users and I need to expand it?

If i don't want to use a Cloud.. I can buy another dedicated server but at that point how can I split the traffic between my 2 dedicated server?

Which is a good strategy for this?

Note: yes i use a database of course (mysql) and no i don't store any session information