Right-side
般 supplies the sound bān with no tone shift.
般 itself shows
舟 (boat) +
殳 (pole/oar) — a person poling a boat, originally meaning 'to convey by boat'. The boat-conveying sense is faintly relevant to
搬's 'transport, move' meaning. Same phonetic family:
班 (class/team),
斑 (spotted).