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Multi-speed air handlers are modeled using one of several unitary system objects which have a Fan:OnOff child component. The unitary system controls the speed of the fan to meet the load.
For a multi-speed air-to-air heat pump or multi-speed furnace with DX cooling, use AirLoopHVAC:UnitaryHeatPump:AirToAir:MultiSpeed. This can be used with the standard thermostat or with a staged thermostat. See example files AirflowNetwork_MultiZone_House_TwoSpeed.idf, MultiSpeedACFurnace.idf, MultiSpeedHP_StagedThermostat.idf, and others. But this unit does not support humidity control.
AirLoopHVAC:UnitarySystem can model the same options plus it supports humidity control (but there are not as many example files yet to show these combinations). For the type of humidity control you describe, use Coil:Cooling:DX:TwoStageWithHumidityControlMode and Dehumidification Control Type = MultiMode.
Note: I think there is an error in the documentation which states that MultiMode only works with cooling coil type = CoilSystem:Cooling:DX:HeatExchangerAssisted. I am checking on this.