right now I have all of my car audio working off of a old 400watt computer power supply I had laying around inside of my house (using as a home stereo system). However, although the system has been working flawlessly for weeks, the amp is a 600watt max power amp and thus under songs which have a lot of continuous bass, the power supply will kick out until I lower the volume because it cannot handle the continuous load.

now, I also have another old 400 watt power supply lying around, which when combined with the other power supply (if possible), would solve my power needs. After some searching, I found a few topics saying that wiring two power supplies together would be bad. However, the simple laws of circuits tell me that if I wire the two power supplies in parallel, ill be able to keep the voltage at 12v, but increase the amps, and hence increase the watts available to the amplifier. Am I missing something stupid? Why would this not work? Does anyone have any ideas as to why this might cause something to blow up?

Do not do it with a PC power supply. Their outputs are not diode protected, and they will "feed" off one another. You can use a larger analog power supply, or get a larger PSU, but don't attempt to parallel two computer supplies...

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

Well the aim of the project was to spend no money and just use old supplies. What about if the 12v rails were both rated at the same amperage?

No. They are not diode isolated or protected outputs, so you cannot parallel them. I assure you, bad things WILL VERY LIKELY happen. Your BEST case will be that you blow the fuse inside one or both of them, then you're tearing them apart to replace them. You show that one of them is a 26A capacity... Is that the one you are using presently?

If you need more current, and you are using just one output wire from the power supply, you are most likely only using one of the 12V rails within the PSU. Parallel all of the yellow wires on ONE power supply to be sure you are using all of the 12V current the power supply can provide, but do not parallel a second PSU. Parallelling the rails within one unit is OK, I've done it myself, but you'll damage stuff (as I have also done) if you try to parallel secondary PSUs.

What is the EXACT power supply make and model you are using? I'll see what I can come up with regarding specs on it.

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It all reminds me of something that Molière once said to Guy de Maupassant at a café in Vienna: "That's nice. You should write it down."

If you diode isolate the supplies, you will be fine.  This will drop the voltage by about 1/2 volt.  But it will definitely be safe for your application.  However this will allow you only 40 amps of current.  Not the 46 you are thinking.  At 40 amps for brief periods you will probably be OK.  At 42 amps, one supply will be trying too hard. 

https://www.surplussales.com/Semiconductors/Diodes-3.html

Stud Diode 45 volts @ 75 amps

I think you will be allright without the diodes, but just to be safe.  You will need 2 of the above.  And a piece of aluminum flat bar to mount them into to use as a heat sink.  Cathode towards the amplifier. 

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Let's Go Brandon Brown. Congratulations on your first Xfinity Series Win. LGBFJB