Voltage regulator IC with external reference
The requirement basically translates to the ability to source high current at a specified reference voltage. 

A low component count way to implement this is to use a high power high current op-amp as a voltage follower, with the reference voltage at the non-inverting input.

For instance, the Burr Brown (now TI) OPA549 can deliver 8 Amperes continuous current with a suitable heat sink. With its 300,000 open loop gain, this should be sufficient for using the available low current reference to generate a stable high current output.

There are many other such high current op-amps, which dispense with the need for the external MOSFET. 

From this page:



In other words, a voltage regulator IC is not required.