At the expense of dissipating even more heat in the supply, here a way of boosting the output to ~5A. In this sim, Pot=0.5K, meaning that the output is 3V (green trace). The power dissipations go from sublime to ridiculous. Q1 is dissipating 125W (red trace), '317 is dissipating 30W (blue) all to deliver 15W to the 5A load (violet). Efficiency = 15/(125+30) = 9.7%

The current booster is shown on some old app notes. With R5 = 1Ω, about 1A of the load current goes through the '317, while 4A goes through Q1.

 

No design is worth a damn until you check the transient response for overshoot and stability. Here the supply is set for ~15.3V, and the 5A load is switched on and off at 10ms and 65ms.

Note the damped response (a tribute to how I placed C3 and C4). There is a bit of ripple evident when the supply is loaded with 5A (from 10 to 65mS). All in all, not too bad.

btw- maybe some of you LTSpice skeptics out there have gotten the message about how good LTSpice is in doing "what-if" analysis like this. Try this with some of the toy simulators; you know, the ones that force you to put a oscilloscope in your circuit just to see a waveform...