A simple method is presented for generating multicomponent Schrodinger cat states through resonant atom-field interactions. In the scheme n two-level atoms, initially in ground states, are sent through a resonant cavity filled with a strong coherent field sequentially. Then state-selective measurements are performed on the atoms. The detections of the atoms in ground states collapse the cavity field onto a superposition of 2n coherent states. This is the first way for producing superpositions of many coherent states through resonant atom-field interaction.