  We study self-interacting dark matter coupled to the Standard Model via the
Higgs portal. We consider a scenario where dark matter is a thermal relic with
strong enough self interactions that can alleviate the problems of
collisionless cold dark matter. We study constraints from direct detection
searches, the LHC, and Big Bang nucleosynthesis. We show that the tension
between these constraints and the need for sufficiently strong
self-interactions with light mediators can be alleviated by coupling the
mediator to either active or sterile neutrinos. Future direct detection data
offers great potential and can be used to find evidence of a light mediator and
verify that dark matter scatters via long-range self-interactions.
