Is it possible for asthma patients to be prescribed more than one relief medication?

Yes: Asthma is an inflammatory airway disease that occasionally causes reversible obstruction of the airway. Immediate relief is necessary for reversal of obstruction but anti-inflammatory agents are used to control inflammation of the airway. Key to control of asthma is control of inflammation to prevent airway remodeling hence need for chronic polypharmacy / immnuotherapy.