Let X be a point process and let F 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 F. In particular, the progressive enlargement is done by means of a whole point process H. We work here in full generality, without requiring any further assumption on the process H and we recover the special case in which X is enlarged progressively by a random time τ.