LM317 based voltage regulated high current power supply problem
The use of PNP pass transistor(s) will improve the circuit. 







simulate this circuit &ndash; Schematic created using CircuitLab

Paralleling multiple transistors is perilous because the warmest of them
passes more current (and heats, and goes into thermal runaway).   Emitter resistance here is good, promotes equal current sharing.  The base of those power transistors SHOULD have a base-emitter resistor to turn them OFF reliably if they get hot.

The series diode and NPN base-emitter
junction decouple the output voltage from the feedback sensing (which lowers the regulation accuracy), but the PNP driven off the input pin does not interfere with the normal output sensing.

For low currents, the PNP transistors just turn OFF; at high current,
they pass at most 4x the regulator's current limit (LM317, about 1.5A).

D2, D3, D4 are optional, to prevent reverse voltages when power is turned off.

Leaving one end of the potentiometer open is not recommended, because adjustment during operation can open-circuit the wiper for a short time,
and limiting that glitch (or adding a capacitor to limit its slew rate)
is good practice.