Wedge‐shaped molecules, such as dendrons, are among the most important building blocks for directed supramolecular self‐assembly. Here we present a new approach aimed at widening the range and complexity of potential mesophases by introducing double‐tapered mesogens. Two series of compounds are presented, both alkali metal salts (Li, Na, Cs) of 3,4,5‐tris‐alkoxybenzoic acid with a second tapered tris‐alkoxyaryl group attached at the end of an alkoxy chain. The double‐tapered compounds all display an unusual hexagonal columnar phase consisting of one ionic and three non‐ionic columns per unit cell. The cation size has an unexpectedly drastic effect on unit cell size. Unlike most columnar phases, the current phases show unusually high dimensional stability on heating, and high stiffness in spite of being 80–85 % aliphatic, attributed to their molecular topology. The described approach may lead to co‐assemblies of multifunctional materials, for example, parallel p‐ and n‐semiconducting nanowires or parallel ionic and electronic conductors.