Boxy, peanut-or X-shaped "bulges" are observed in a large fraction of barred galaxies viewed in, or close to, edge-on projection, as well as in the Milky Way. They are the product of dynamical instabilities occurring in stellar bars, which cause the latter to buckle and thicken vertically. Recent studies have found nearby galaxies that harbour two such features arising at different radial scales, in a nested configuration. In this paper we explore the formation of such double peanuts, using a collisionless N-body simulation of a pure disc evolving in isolation within a live dark matter halo, which we analyse in a completely analogous way to observations of real galaxies. In the simulation we find a stable double configuration consisting of two X/peanut structures associated to the same galactic bar-rotating with the same pattern speedbut with different morphology, formation time, and evolution. The inner, conventional peanut-shaped structure forms early via the buckling of the bar, and experiences little evolution once it stabilises. This feature is consistent in terms of size, strength and morphology, with peanut structures observed in nearby galaxies. The outer structure, however, displays a strong X, or "bow-tie", morphology. It forms just after the inner peanut, and gradually extends in time (within 1 to 1.5 Gyr) to almost the end of the bar, a radial scale where ansae occur. We conclude that, although both structures form, and are dynamically coupled to, the same bar, they are supported by inherently different mechanisms.