The "Open Primary" and Other Systems
"An Alabama Independent" commented at Ballot Access News: "… we need to have… a single 'OPEN PRIMARY'… . For in a single 'Open Primary' the top two candidates go into the general election – or, such can be designed where at least the candidate of each political party with the most votes in the primary – go into the general election. (There then can be such a thing as 'top two,' 'top three,' 'top four,' etc…"
You have mixed the “top two” with the blanket primary. As a nonpartisan system, the “top two” does not include a nominating process, although each party has the option of endorsing candidate(s). And, instead of a “top two,” there could indeed be a “top three,” a “top four,” etc., although I’m not aware of any nonpartisan system having been used other than the “top two.”
In a blanket primary, all candidates of multiple parties are listed on a single primary ballot, and the top vote-getter from each party advances to the general election, where any independent candidates are also on the ballot.
Jim Riley and I have frequently mentioned on this site California Democratic Party v. Jones (2000), in which the U. S. Supreme Court struck down the state-mandated blanket primary.
In a system of open primaries, each voter picks a party on primary day. Much of the reasoning in Jones also applies to the open primary, which is why I predict that, when a suit challenging the state-mandated open primary reaches the U. S. Supreme Court, the justices will also declare it unconstitutional.
Click here for an article on the various election setups, including the “top two” and the party primary systems. Links to the Jones ruling are featured under “Blanket Primary.”
 The "top two" is also popularly called the "open primary." All candidates, including independents, run in the same election. The top two vote-getters, regardless of party, move on to the runoff (I'm always amazed when an independent praises the "top two," since it makes it nearly impossible for independents and small-party candidates to get elected).