Power feeder scheme adaptation
While this does not seem to be a typical regulator boost circuit, I do see the basic idea.  With some adjustments it should work fairly well, though stability could become an issue.

First off, the PNP is not wired correctly, the emitter-collector connections should be reversed.  With the pins corrected the PNP will turn on when R1 is passing about 375ma, (0.375 x 1.6 = 0.6).  Now when the PNP passes enough current through R8 the NPN parts begin to turn on.

The next potential problem is with the NPN parts.  As connected they may not turn on equally.  The NPN with the lowest Vbe(turn on) will begin passing current first and the others may turn on later and pass less current.  To better equalize the NPN's you could add very small resistors onto the emitter of each one, (just 0.1 ohm @1w should do), this will help to even out the current through each.  

You didn't list the regulator type, (Perhaps LM317 ? But the output would be only about 3v with those resistor values, you may want to verify this).  

Depending on your output voltage the NPN parts will likely require good heat sinking.  The dissapation will be nearly ((24v-Vout) x (Iout/4)).  

You may need to do some additional tweaking of resistor values to get the best stability.  A potential improvement may be to add capacitors of 50uf-100uf at each end of the regulator.

For more typical regulator boost circuits see:
http://dc-voltage-regulator.blogspot.com/2012/12/high-current-7812-voltage-regulator.html
http://www.reuk.co.uk/LM317-High-Current-Voltage-Regulator.htm