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Unless the plug-in is written in an unusual manner, every instance is separate.
Some plugins that use DSP cards might do things a little differently, but unless the plugs are designed to do something behind the scenes like sidechaining or a rewire type setup, each instance should always be totally independent of the others. There's no difference, technically, from running a different plug on each channel.
Of course, if a plug has a distinctive sound, that might cause some stacking of some frequencies, etc.
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