connecting multiple PSUs together to supply different rails???

I was given an old audio processor but it doesn't have a psu.
It requires +/-12v DC, and 5V DC. Unlike most computer psu's a high current -12v rail is required.
I can't find an off-the-shelf PSU that will provide exactly what I need so I was wondering if I could use multiple PSU's to do the job?
So If I have 2 x 12v psu's and connect the + from one to the - of the other that gives me the +/-12v I require.
I have another 5v psu I can use, so should I connect all the 0v points together?
Here is a rough diagram that will hopefully explain what I mean:
PSU example.png

Please let me know what you think.
I think the middle part on the bottom side has the wrong polarity: -12 V is connected to the + terminal and 0 V to the - terminal.

Are you sure your supplies have floating outputs, or are there ground or earth connections hidden somewhere that short all negative terminals of the supplies?
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