If a chip with multiple amps exists you will get better results. When circuits are fabricated on the same wafer, right next to each other, they will usually perform identically (or nearly so).
A 2nd option might be using a PLL (phase locked loop) to keep the signals in phase.
Hope this helps.
I've had to make do with a couple of 2 ch. scopes on occasion. That gives me a 4 ch. 'logic analyzer'. If you're looking for a learning aid and you have access to class labs facilities you might be able to get more channels. I would would write a tight little loop to be able to view the signals...