This will depend on the Wattage of the case fans. Each fan channel of the Smart Device can support up to 10W of power. Exceeding 10W will result in buggy or inconsistent performance, and/or a total shutdown of the channel or device.
For reference, our H-series cases include our Aer F fans. The 120mm version of this fan uses 2.16W per fan, and the 140mm version uses 3.84W per fan. As such, each fan channel of the Smart Device can control up to four 120mm fans, or two 140mm fans.