<p>Recently, there has been a growing trend toward exploring and exploiting new/additional degrees of freedom in optical beams. This is particularly relevant in the field of multiplexing optical data transmission channels and in the interaction of laser radiation with matter. In this paper, we explore two aspects of additional degrees of freedom in axisymmetric binary elements. The first is the generalized phase dependence on the radius, which leads to variations in the longitudinal beam distribution. The second degree of freedom is associated with the binarization effect, which generates multiple axial diffraction orders. Control of these orders is proposed by introducing a vortex component in the illuminating beam. More specifically, we consider binary axisymmetric and vortex generalized axicons which are optical elements with different power-law dependence of the phase on the radius. Formation of additional axial diffraction orders associated with binarization leading to complex interference distributions on the optical axis is studied analytically, numerically and experimentally. Selection and compensation of such diffraction orders is much more complicated than off-axis ones (which can be simply isolated with an opaque screen), but their use provides a 3D character of control over the distribution and multiplexing of laser beams. It is shown that the use of vortex illuminating beams allows one to effectively solve the problem. At the same time, the allocation of high diffraction orders provides a proportional decrease in the size of the light spot on the optical axis. The experimental results fully confirm the obtained modeling results. The studies performed in this paper can be useful for variations in the size of the focal region, 3D (de-)multiplexing and coding.</p>