Multiple amps + single power supply = unstable output

Hi all -
I am testing some amplifiers (very basic INA217 configuration) and I've noticed something very unusual (or unexpected at least).

When I am trying to amplify 1 signal on 1 amplifier, the results are coming back very nearly as expected. When I am trying to amplify 2 different signals on 2 different amplifiers, the results are all over the place; the output is totally unstable.

I am using a PC power supply moded to a bench power supply (http://www.hackaday.com/entry/1234000687042947/). This is for testing purposes only. For the experiment, I am planning on using pairs of 9V batteries for each amp (there is a total of 4 amps).

Now I am also going to be adding some high pass butterworth filters to this, which is also going to require power. Is there something I can do that will allow me to use the same power supply for more than one amplifier or 1 amp and 1 filter?

Thanks,
-- Mike