Building on a pre-existing line of inquiry where the presence of solid particle attractors in thermovibrationally driven flows was demonstrated in cavities subjected to a unidirectional temperature gradient, the present work considers cases where the direction of such a gradient is allowed to change inside the fluid. Moreover, the considered configurations differ with regard to the angle that vibrations form with respect to a reference axis. Variations in the orientation of the temperature gradient are made possible by setting a non-uniform temperature distribution along certain walls. The relationship between the multiplicity (N) of the loci of particle attraction and the inhomogeneities in the temperature field is studied. It is shown that N can exceed the limit N = 2 found in earlier studies and that a zoo of new particle accumulation structures show up, whose ranges of existence depend on the amplitude and frequency of vibrational acceleration, the particle Stokes number, the orientation of vibrations, and the number of inversions in the direction of the temperature gradient.