We consider agglomerates of misaligned, pressure supported tori orbiting a Schwarzschild black hole. A leading function is introduced, regulating the toroids distribution around the central static attractor - it enables us to model the misaligned tori aggregate as a single orbiting (macro-)configuration. We first analyse the leading function for purely hydrodynamical perfect fluid toroids. Later, the function is modified for presence of a toroidal magnetic field. We study the constraints on the tori collision emergence and the instability of the agglomerates of misaligned tori with general relative inclination angles. We discuss the possibility that the twin peak high-frequency quasi-periodic oscillations (HF-QPOs) could be related to the agglomerate inner ringed structure. The discrete geometry of the system is related to HF-QPOs considering several oscillation geodesic models associated to the toroids inner edges. We also study possible effect of the tori geometrical thickness on the oscillatory phenomena.