Is there any way to maximize PHP_INT_MAX?

No.

From http://www.php.net/manual/en/reserved.constants.php:

These constants are defined by the PHP core. This includes PHP, the Zend engine, and SAPI modules.

Nope. It's hardware/os limitation, not PHP.
You can use bcmath fructions for large numbers

You can increase PHP_INT_MAX. As others have said, PHP_INT_MAX is platform dependent. That means on 32 bit hardware or a 32 bit OS or a 32 bit compile of PHP, PHP stores the bit in 4 bytes (max of about 2 billion). However, if all 3 are 64 bit, the max goes to 8 bytes (about 9e18 or 9,000,000,000,000,000,000).

So if you really want large ints, get a 64bit machine, and a 64bit OS, and a 64bit compile of PHP...

You can not control it actually. However, if you are dealing with BIG numbers, I would suggest you the:

BC Math extension.