Well, in a three body system at least. One could design a four body (or more) system such that the gravitational centre, the orbiting tidally-locked body and a gravitationally bound body orbiting the tidally-locked body were all static, given the influence of another body very specifically placed to keep the 'orbiting' one in the shadow perpetually.

Without crunching the math though, it would be a terribly weird system and likely with the orbiting body being very far from it's parent and essentially hovering between orbiting the solar mass and its planet. That and requiring a massive object in a leading orbit at a significant distance from the planet in question.

The whole thing would be jittery as hell but plausible in a spherical cow sort of way. (In retrospection, it might well require a series of increasingly massive bodies in increasingly interesting orbits. I still maintain it is plausible in a purely theoretical way but in no way feasible to occur through nature or design.)