Thank you for your post.
The main limitation in trying to use more than one Oscilloscope is that Picoscope will only support the use of one scope and therefore only show 2 channels. It is also not possible to run more than one instance of the software at a time. Therefore you cannot use the Picoscope software to measure all 3 phases.
You can however use multiple converters with the Picolog software, this would enable you record from all 6 channels. However, you are limited to using Real Time Continuous Mode, which in turn limits you to a maximum sample rate of one per millisecond.
I would advise that the best way to measure all three phases would be to use seperate computers, this way you still have the same amount of flexibility with software that you do when measuring one phase.
Hope this helps