Magnetic chiral skyrmions are particle-like excitations with a topological charge, which are currently considered as promising objects for the next generation of magnetic memory, logic, and neuromorphic devices. In three-dimensional systems, they can form rather complex topological structures. In bulk helimagnets, elongated skyrmion tubes can be ordered either perpendicularly or parallel to an external magnetic field and such configurations coexist in a specific range of fields. We have shown that with an increase in the magnetic field, the transition from perpendicular to parallel ordering in a 3D skyrmion dimer occurs through an intermediate state with mutually orthogonal skyrmion tubes. In the system with three and more skyrmion tubes, we uncovered a surprisingly large diversity of superstructures and systemized the principles of their formation. The nascent conical state is shown to induce the field-dependent switch between favored skyrmion clusters and underlies attracting inter-skyrmion potential. We argue that our numerical simulations on skyrmion clusters are valid in a parameter range corresponding to the A-phase region of cubic helimagnets. Moreover, skyrmionic superstructures constitute a novel concept of spintronic devices based on gapless skyrmion motion along with each other.