If you want to be hyper-technical about it, he could order a hit on Trump, but if Trump was already on the ballot and received 270+ EVs, he would be ineligible to be President. His Vice President would take over as President.

If both were assassinated, the Speaker of the House of the newly-seated Congress would become President.

I don’t think you meant that specifically, but yes if ordering a hit is an “official act”, he could conceivably order the murder of anyone who cares to stand against him.