At 24V there will probably be an over-voltage circuit that will kick in, the excess stress on the output rectifying device will be close to killing it, and if you draw the same o/p current you will be trying to draw double the design o/p watts, so the thing will trip on over-temp if you are lucky (just plain BANG if unlucky), the output caps may not be rated for 24V either...
2 x ATX psu's with the 12V connected in series will give you 24V at design o/p current...