The problem with paralleled regulators is that the current sharing isn't equal without some additional means of keeping them balanced. (Usually a low-value resistor on the output of each.) The datasheet should have suggestions on using external transistors for high(er) current applications, which is a far better (and usually simpler/cheaper) way of improving current capacity.
As it stands, one of those ICs is doing more work than the rest. As such, when you load them down, it will fail first. And then the second most aggressive IC will take the brunt of the load, and fail shortly after. Then the next will die very quickly. And the next...
The only reasonable way to generate a variable 20A supply is with a beefy switching regulator design that can vary its PWM duty cycle enough to provide the voltage range you want. Although, you then have to compromise on the output filtering stage, rather than tuning it for a particular voltage or small range of voltages. With higher-current supplies, this balancing act gets more complicated. Which is why you probably won't find many out there.
Seriously, any time you're talking about 20A regulated supplies, it should ring alarm bells. Why do you need 20A? Typically, with that large of a load, it either 1) doesn't really need to be regulated (e.g., relays, motors, heaters, lights, power amplifiers, etc.); or 2) is a large project that can probably be broken down into more, smaller power supplies (e.g., a car computer where you can supply power to drives separately from the motherboard, and probably get by with a low-power CPU like an Atom or VIA EPIA).
Finally, there's good reason not to have that much power on tap. A short circuit on a 3A supply will blow an output fuse or kick it into over-current protection. With a 20A supply, depending on the resistance between the supply and the fault, you could set things on fire while the supply just keeps on truckin' like nothing happened.