Our house (has 4h2c) for example is set up to bring on 1st stage cool with a 1 degree rise and second stage cool with a 2 degree rise. If the humidity is above 50% then it runs second stage compressor but leaves the blower on first stage cfm. The heat pump runs seconds stage if the outdoor temp is between 32 and 50, first stage hp only if it's over 50,first stage gas if it's 31 or less and second stage gas if the stat falls 2 degrees below set point.
One simple solution for 3 cooling stages is to use the dehumidification terminal to drop out 2nd stage. Otherwise you normally cycle between 2nd and 3rd stages. The airflow would have to by managed by the air handler(s). But airflwo requirements would depend on how many refrigerant circuits it has and how the coils are configured.