Multiple PHAT DAC boards?

On a Raspberry Pi 3B, can I install multiple PHAT DAC boards and get two, or even more, stereo audio outputs? This includes not only handling multiple I2S interfaces, but also sufficient CPU to service them, without glitches. I know I’ll have to wire the pins differently for the additional boards.

Then the same question for a Pi zero.

My application simply generates a different sinewave to each channel, forever. The more channels per PI the better. So there is no software encode/decode, just a loop for each channel filling a buffer with the (stereo) sinewaves from a table, and writing them to the device, for each device. This is the only thing the PI needs to do (not even terminal or WiFi I/O, once the program is installed).

This is to drive a scientific instrument, and high-quality audio is necessary. Ultimately I need 5 different sinewaves, so three PHAT DAC boards if their stereo separation is sufficient, five if not. Space is at a premium.

There’s only one I2S data pin on the Pi, so that kind of scuppers the whole thing. :-(