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, including those in Congress who might wish to impeach him or remove him from office.