He is the leader of the house, and has a majority. He can initiate a process for relevant rules as a majority leader for his removal or simply submit a motion in this regard. There is nothing unusual in that -
In the western democracies, it is the parliaments that remove, dismiss its members after internal investigation and internal trial by its member' voting (Our constitution will require a report to EC by the speaker. and EC can remove)-
Self-accountability is considered to be necessary for the independence of the parliament. However so-called Pakistan democracy is unique - perhaps it mainly a self-serving club.
Yet I don't think PM should take that course due to some negatives. We are not at a stage of democratic institutions that parliament can become self-accountable (by the majority vote) without a controversy - So what is generally thought to be needed for stabilizing and to strengthen the institution. in Pakistan it will weaken it in our kind of politics. At present vested groups are in the grip of the criminals who will fail it. If PM has to take action, better yo go through courts as only courts have some weight to counter the criminal groups -
IMO opinion PM/government shouldn't press any charges at all. In a political discourse, this issue will be sorted out and all misguided blackmailers will be neutralized in due course.