The Fair Representation Act
There is currently a bill proposing the use of a variant of STV in multimember districts. Called the Fair Representation Act, it mandates districts with no more than five representatives per district. Within a district, winners would be chosen by STV. States with up to five representatives would have a single district. States with six or more would be split into three, four, and five member districts.
It also changes how districts are drawn, mandating a commission.
This is just a law. No constitutional change needed.
One district per state
Another alternative would be to make each state one district. Then there could be as many winners as there are representatives for the state.
The Fair Representation Act's limitation to five member districts means that it is difficult for smaller parties to get representation. It would help Democrats in Republican states (like Louisiana) and Republicans in Democratic states (like Massachusetts). But it wouldn't help Libertarians or Greens, as they don't pick up enough of the vote to win a seat. At least it wouldn't based on the presidential results in 2016, when the best third party result was Gary Johnson's 9.34% in New Mexico. Perhaps they would get more support if winning was feasible.
Statewide districts would give smaller parties a chance to win in larger states. California is large enough that even 2% of the vote would give enough of the vote to provide a seat. More like 3% for Texas, Florida, and New York. A five member district is around 16.7%. 20% and 25% for four and three member districts.
Statewide districts would eliminate the need for drawing district lines altogether. Voters would be in complete control of the process.
Of course, the existing two parties may not find it in their interest to switch to larger districts like this. They could do it with just a law though. Or they could repeal the existing law preventing states from doing so on an individual basis.
In theory, there could be a national district with 435 representatives. But currently the constitution mandates that representatives be apportioned to the states. So an amendment would be necessary to change that.
Absent a constitutional amendment changing how Senators are apportioned, Senators can not be selected by Single Transferable Vote (STV). Senators are directly elected by the voters of states, one at a time. Each state has two Senators who are elected in different years, as per the constitution.
Senators could be chosen by a ranked voting method like you suggest for presidential races. States could choose to do this on an individual basis or Congress could mandate it nationally if they can find a constitutional basis (e.g. respecting minority votes).