Switching from mod_php to php-fpm + proxy-fcgi (ie still with Apache) and then using the event mpm will help a lot.
Putting varnish in front of any web server will help more.
Putting varnish in front of any web server will help more.
This has been my goto implementation because it can be rapidly deployed. Shameful plug: I've built Cachoid [0] for this very reason. It's a Varnish as a service platform and you can get up and running within 10 seconds.