Three questions, so three answers.
1. "One extra power supply would give twice the current at the same voltage by connecting two of them with their 12 volt 10 amp outputs connected in parallel and with the third power supply 5 volt 20 amp output in series to get a total output of 17 volt 20 amp"
Answer ...yes no problems with this, just isolate the earthing inside on the secondary of the board only. You should see the "lands"(copper/tinned areas) that interface with the chassis on the output side. Leave the input side earthed, this is part of the noise reduction filter...not necessary, but nice.
2."That's the easy part, but wouldn't their inputs (115-230 volts)interface in some way with their now floating outputs earths which are connected to the chassis?"
Answer These supplies are what's known as offline supplies. There is no connection in any way of the secondaries - to the Mains input side. When you lift the secondary away from the earth, the floating outputs are completely isolated from the mains in all useful ways. (sometimes they have a very small capacitance cross connecting, but only a few picofarads)
The primary sides (110v in your case) are going to be connected in parallel, and so it does not matter that the primaries are earthed. ( forget for the moment that the neutral is earthed at the switchboard ).
You have correctly pointed out a weakness in my previous reply. When I first did this, I opened them up and parallel wired them for single powerpoint operation. I didn't connect the earths up, as they were to be together in a single chassis, and the chassis would be earthed. In my case I remember only that I put cardboard under them, and it all worked. This memory wrongly led me to say that seperating them would solve the problem....it did for me, but I hadn't considered all cases..... so if you disconned the secondaries from chassis ("O" rings under the board or similar, you will have no troubles.
3." >>>The atx supplies bring a whole lot of other considerations, so stick with the at supplies.<<<
Why wouldn't any PC power supply work when connected in this way?'
Answer. Yes. Same rules apply with the un-earthing of secondaries. You would have to ground the grey wire I think, in order to wake up the supply and light up the main PWM.(I'm going with Amanda's excuse here.. It's been a few years since I played with them... i think it's the grey one)
The atx is a generation ahead of the simplicity of the at supply. They are more likely to stop you from loading up one voltage rail, without loading up other voltage rails, and may see this as an error. They are more complex with the extra PWM converter providing the sleep power functions, and as I said, have a much higher intergration of safety circutry which may catch you by surprise.
That said, they may well work the same, but don't be surprised if they stop you using certain combinations. They tend to balance the four or five voltages through various voltage dividers, get the sum, and provide that to the error op amps in the tl494, they also send samples to scr shutdown triggers. Depends how they balance these dividers, as to how drawing current from only one of them will affect the error traps. The rotten things are all different, so some will be great, some may be finnicky, all will work to some extent.
Have a look at that link i left, with four resistors, and one capacitor, you may get one supply to do your 17v at 15A or more...cooling dependant. It is interesting, that the diode in this instance are the 12 volt rails diode. Usually rated at 8A, but under pwm, easily handle 20A I guess its the duty cycle, but I don't really know.
Have fun with this..........oztules