  We explore the self-interacting dark matter scenario in a simple dark sector
model where the dark matter interacts through a dark photon. Splitting a Dirac
fermion dark matter into two levels using a small Majorana mass can evade
strong direct detection constraints on the kinetic mixing between the dark and
normal photons, thus allowing the dark sector to be more visible at high
intensity and/or high energy experiments. It is pointed out that such a mass
splitting has a strong impact on the dark matter self-interaction strength. We
derive the new parameter space of a pseudo-Dirac self-interacting dark matter.
Interestingly, with increasing mass splitting, a weak scale dark matter mass
window survives that could be probed by the LHC and future colliders.
