Systems and methods maintain a fold, e.g., an intussusception, formed in a portion of the stomach wall. In one example, a system includes a holding device that is positioned at least partially in a stomach and receives a portion of a wall of the stomach. The holding device includes a first section connected to a second section. The holding device is operable to move the second section relative to the first section into a position in which a cavity is defined between the first section and the second section. The cavity receives the portion of the wall of the stomach. The system includes a securing device that is positionable around the second section while the portion of the stomach wall is received by the cavity. The securing device is operable to provide a force around the second section to maintain the portion of the stomach wall stably in the cavity.