  A single photon can be made to entangle simultaneously in its different
internal degrees of freedom (DoF) -- polarization, orbital angular momentum
(OAM), and frequency -- as well as in its external DoF -- path. Such
entanglement in multiple DoF is known as hyperentanglement and provide
additional advantage for quantum information processing. We propose a passive
optical setup using $q$-plates and polarization beamsplitters to hyperentangle
an incoming single photon in polarization, OAM, and path DoF. By mapping
polarization DoF to a two-dimensional coin state, and path and OAM DoF to two
spatial dimensions, $x$ and $y$, we present a scheme for realization of
two-dimensional discrete-time quantum walk using only polarization
beamsplitters and $q$-plates ensuing the generation of hyperentangled states.
The amount of hyperentanglement generated is quantified by measuring the
entanglement negativity between any two DoF. We further show the
hyperentanglement generation can be controlled by using an additional coin
operation or by replacing the $q$-plate with a $J$-plate.
