Sheet processing apparatus and image forming system incorporating the sheet processing apparatus

A sheet processing apparatus comprising:

• a tray to receive and store multiple sheet media as a sheet bundle;
• a first binder to press the sheet bundle to bind the sheet bundle at a binding position;
• a second binder to penetrate the sheet bundle with a needle to bind the sheet bundle at the binding position;
• a feeder to:
• feed the sheet bundle in a first direction toward the first binder and the second binder;
• and
• move the sheet bundle in a second direction opposite to the first direction;
• and
• circuitry configured to:
• cause the feeder to move the sheet bundle on the tray in the second direction;
• move the first binder from the binding position to a home position different from the binding position in a width direction orthogonal to the first direction and the second direction;
• and
• move the second binder to the binding position in the width direction to bind the sheet bundle by the second binder after the sheet bundle is moved in the second direction and the first binder is moved to the home position.