  In this paper we generalize the concept of $q$-plate, allowing arbitrary
functions of both the radial and the azimuthal variables, and study their
effect on uniformly polarized beams in the near and far-field regime. This
gives a tool for achieving beams with hybrid states of polarization (SoPs), and
alternative phase and intensity distributions. We also implement an
experimental device based on a liquid crystal on silicon (LCoS) display for
emulating these generalized $q$-plates. Moreover, we propose an application
that takes advantage of the pixelated nature of this kind of devices for
creating arbitrary superpositions of vector and vortex beams by representing
onto the LCoS randomized combinations of two different $q$-plates, i.e.
multiplexed $q$-plates. Great agreement is found between theoretical and
experimental results.
