There is only a mandate for how the electoral votes cast by states determine who becomes president, but now how states cast those votes.
Some states cast them all for the popular winner in that state. Some split them proportionately among the top scoring candidates. Some states have agreed to a pact that, if enacted by enough states, will switch those states to casting their votes for the national popular vote winner.
https://en.wikipedia.org/wiki/National_Popular_Vote_Intersta....
In theory a state could hold ranked choice votes among any number of candidates and cast their electoral votes for the final ranked choice winner.
Even the primary system is something managed at the state level.
So a lot could be done but it requires changing state laws or potentially state constitutions.