One-dimensional (1D) boron nitride nanotube (BNNT) and 2D hexagonal BN (h-BN) are attractive for demonstrating fundamental physics and promising applications in nano-/microscale devices. However, there is a high anisotropy associated with these BN allotropes as their excellent properties are either along the tube axis or in-plane directions, posing an obstacle in their widespread use in technological and industrial applications. Herein, we report a series of 3D BN prototypes, namely, pillared boron nitride (PBN), by fusing single-wall BNNT and monolayer h-BN aimed at filling this gap. We use density functional theory and molecular dynamics simulations to probe the diverse mechanomutable properties of PBN prototypes. Our results demonstrate that the synergistic effect of the tubes, junctions, and sheets imparts cooperative deformation mechanisms, which overcome the intrinsic limitations of the PBN constituents and provide a number of superior characteristics including 3D balance of strength and toughness, emergence of negative Poisson's ratio, and elimination of strain softening along the armchair orientation. These features, combined with the ultrahigh surface area and lightweight structure, render PBN as a 3D multifunctional template for applications in graphene-based nanoelectronics, optoelectronics, gas storage, and functional composites with fascinating in-plane and out-of-plane tailorable properties.