...parties than the current? system?

With approval voting, the nation would get a ballot with list of all candidates of all parties and all independent candidates. Next to every name would be a "Yes" and a "No" check box.

You get to choose whether you approve or disapprove of each of the candidates and the candidate with the most "Yes"s wins.

Would this not permit candidates from all backgrounds to compete in a more equal footing and provide America with more choice of candidates?

(In case anyone brings up the objection of the electoral college, we don't have to have an electoral college. The constitution has an amendment process and we can amend it if we think that it is to our benefit).