Let X be a point process and let X denote the filtration generated by X. In this paper we study martingale representation theorems in the filtration G obtained as an initial and progressive enlargement of the filtration X. The progressive enlargement is done here by means of a whole point process H. We do not require further assumptions on the point process H nor on the dependence between X and H. In particular, we recover the special case of the progressive enlargement by a random time τ.