Suppose there was an American third party candidate, who won a quarter of the popular vote, and a single large state or a handful of smaller ones: specifically with enough electoral votes so that neither the Republican nor Democratic candidate could get to "270" in an otherwise close Presidential election. Then the election would be decided by Congressional delegations in the House of Representatives.

Could some of these House delegations vote for the independent candidate if they agreed to do so? Or are the individual members "bound" to the candidate of their own party?

Suppose either the Democratic or Republican candidate wanted to support the third party candidate to deny the other opponent the election. Could this candidate ask "his" state delegations to vote for the third party candidate to help him form the needed majority?

Note: My question is whether the above would be allowed under the Constitution or other relevant "rules of the game," NOT whether it would be "politically feasible."