The invention relates to a support device suitable for being installed in an arrangement referred to as “mounted” against the rear of a back of a seat comprising a headrest. The headrest is held at the top of the back by at least one upright. The support device includes a framework suitable for being positioned and supported on the top of the back, a clamp movable in relation to the framework, and at least one reversible fastener making it possible to fasten the clamp to the framework so as to immobilize the framework in relation to the upright.