  Here, the entanglement entropy is calculated at the quantum multicritical
point of the random transverse-field Ising model (RTIM). We use an efficient
implementation of the strong disorder renormalization group method in two and
three dimensions for two types of disorder. For cubic subsystems we find a
universal logarithmic corner contribution to the area law b*ln(l) that is
independent of the form of disorder. Our results agree qualitatively with those
at the quantum critical points of the RTIM, but with new b prefactors due to
having both geometric and quantum fluctuations at play. By studying the
vicinity of the multicritical point, we demonstrate that the corner
contribution serves as an `entanglement susceptibility', a useful tool to
locate the phase transition and to measure the correlation length critical
exponents.
