It has been pointed out that conflict of interest laws often exempt the President. It also seems, that media coverage notwithstanding, the President-Elect and his team purport to be unconcerned about the massive lurking potential conflicts in almost any action Trump might take domestically or internationally. (Does that sound like an overstatement? If you think so, I challenge you to find an action that he might take or not take that will not impact one or other of his business interests, positively or negatively, directly or indirectly.)
So, aside from the fact that other legal protections do put some constraints on Trump, we might start thinking again about the impeachment power, at least for after either 1) a wave election in 2018, or 2) Republicans finally figuring out that they have been totally conned, or 3) both of the above.
There has been, of course, endless debate about the meaning of the Impeachment Clauses, but what we do now is that their meaning is subject to a lot of change depending on whose ox is going to be gored.
At a minimum, however, there is surely an argument that when the law exempts Presidents’ behavior from being regulated, for something that is surely profoundly wrong, there is a stronger argument for treating it as within the scope of impeachment. I suspect that many of the English impeachment cases were about personal enrichment. The above link references one case of an allegation of payment to Lord Palmeston by the Tsar of Russia.