Apparatus and methods for endoluminal advancement are described herein. A shape-lockable tissue anchoring assembly generally has an elongate body, a handle assembly, and an anchoring assembly positioned at or proximal to a distal tip of the elongate body. A distal portion of the elongate body may optionally be steerable or curvable. The anchoring assembly may include various expandable (30) or projecting anchoring features to contact and retain tissue relative to the elongate body such that pleated tissue is temporarily immobile relative to the elongate body. This anchoring can be actuated simultaneously with or independently from shape-locking of elongate body. The anchoring assembly can be actuated simultaneously with the shape-locking of the elongate body. Alternatively, the steerable distal portion of the elongate body can be angled against the pleated tissue to retain it while the endoscope is advanced relative to the pleated tissue.