Multimember districts need to be considered. In fact I'd like to see the entire house elected at large in each state. Maybe something like you can choose to vote for 50% of the seats, so a 10 seat state would allow voting for up to 5 candidates.
But I'd be very careful with off-the-cuff systems like the one you've proposed. Voting algorithms can behave in surprisingly unintuitive ways when people start voting strategically.
With ranked-choice voting, if
45% voted Trump-Johnson-Hillary,
45% voted Hillary-Johnson-Trump, and
10% voted Johnson-(either)-(either),
then Johnson would have won, despite lacking wde first-choice approval.