One might have thought that the Israel lobby—i.e., the American Israel Public Affairs Committee (AIPAC) and its various associated organizations—had taken pro-Israel advocacy about as far as it could go. Congress routinely defers to the lobby on all matters relating to Israel (including, most notably at this moment, the Iran nuclear issue), while the White House strives to live up to Vice President Joe Biden’s rule that “no daylight, no daylight” (he repeats it) must ever shine between US and Israeli policies.

What more could a lobby want?

More. Just as billionaires keep coming up with ways to make more money, so do lobbies seek ever more power, whether they need it or not. The National Rifle Association proves that point.

The analogy to billionaires and their greed is especially appropriate because two billionaires, Sheldon Adelson and Haim Saban, have recently turned up as key players behind the Israeli-American Council. The IAC was first established in 2007 for the Los Angeles–area Israeli expat community, but the two billionaires are now relaunching it at the national level, hoping to organize the estimated 500,000-800,000 Israelis living in the United States into an AIPAC for Israeli expats—kind of an AIPAC without the A.

The IAC made its Washington debut in November with an “Inaugural National Conference” headlined by the 2012 Republican presidential nominee Mitt Romney and former Democratic senator (and now constant critic of Democrats) Joseph Lieberman. The event followed, and was something of a celebration of, the Republican sweep in this year’s midterm elections.

According to Israeli journalist Chemi Shalev, writing about the new group in Haaretz, the IAC’s goal is “not only to organize Israeli Americans to support Israel but to form an independent political lobbying group that could one day compete and outflank AIPAC itself.” (The IAC’s board chair denies that, and says the goal is not to challenge AIPAC but to strengthen it, although AIPAC has always resisted that particular piece of logic when it comes to its turf.) In any case, the creation of an Israeli-American pro-Israel advocacy organization is an incredible vision, because it takes the AIPAC model and turns it upside down.

AIPAC was established in 1963 because the Israeli government decided that relying on Israelis, registered as foreign agents, to advance Israel’s interests (as is the case with other governments) would not be effective in the long run. Foreign agents must register with the Justice Department. Their activities and spending are monitored, and they cannot involve themselves in American political campaigns.

And so AIPAC was created as an American organization, directed by an American board of directors and with an American membership. It would not (at least openly) take orders from the Israeli government. Although AIPAC’s stand on every issue related to the Middle East would invariably be identical to that of the Israeli government, it would still be able to claim that it was simply promoting the views of its American membership. This set-up also—and this is significant—limits the taint of “dual loyalty” that would accrue if Jewish Americans were seen as following the Israeli government in lock step.

This formula is largely accountable for AIPAC’s success. Had it not been devised, there would have been no way for the pro-Israel lobby to fully insert itself into US policy-making in the Middle East, let alone to direct both individual donors and the various pro-Israel PACS to support or defeat various candidates for office—not to mention keeping the winners in line once they are sworn in. Without that ability, it is hard to imagine that the lobby’s chokehold on US Middle East policy would have ever developed.

Nevertheless, this is the opposite of what Adelson and Saban are pulling off: the establishment of an organization, proud of its Israeli nature, operating in the United States to advance the goals of the Israeli government through political action.

Its genius (if that is the correct word) is that Adelson and Saban are top funders, respectively, of the Republican and Democratic parties, although as Adelson points out, “when it comes to Israel we’re on the same side.”

Adelson was one of Mitt Romney’s top donors in 2012, while Saban is the top donor to and a close associate of Hillary Clinton, the Democratic front-runner for 2016. He says he will spend “whatever it takes” to make her president. So the Israeli-American Council starts with tremendous clout.

But why is it necessary? Yes, Adelson and Saban do employ the kind of extreme rhetoric that AIPAC eschews as counterproductive. Saban, for instance, said at the November conference in Washington that if the Iranians balked at demands to totally eliminate their nuclear potential he would, as a last resort, “bomb the living daylights out of the sons of bitches.” And both Adelson and Saban openly professed a desire to limit media criticism of Israel by agreeing that they should find a way to purchase The New York Times and bemoaning their failure to snatch up The Washington Post when it was recently on the market.

AIPAC is not nearly that blunt (or honest) about its desires, but for the most part, it more than gets the job done. Look at how the United States responded to Israel’s Gaza onslaught this past summer: Congress overwhelmingly supported it, with less than a dozen legislators even offering sympathy to the Gazans. As for President Obama, he repeatedly emphasized Israel’s “right to defend itself,” even though that—as opposed to the strangulation of Gaza—was hardly the issue. Why isn’t all that good enough for Adelson and Saban?

The answer is simple. The lobby, effective as it is, does not have their names on it. It’s just AIPAC, or “the lobby.” As Adelson demonstrated during the Romney campaign, he wants Republicans to think only of him when it comes to matters relating to Israel or funding from its friends. This was demonstrated early this year, when he had potential Republican candidates for president audition before him in a Las Vegas event that the media dubbed “the Adelson primary.” In fact, Ohio Governor John Kasich made clear that even in a room full of Jewish millionaires and billionaires, only one mattered, addressing his audience repeatedly as “Sheldon.” And when New Jersey Governor Chris Christie horrified the right-wing crowd by referring to the occupied territories as occupied territories, it was to “Sheldon” that he directed his mea culpa.

The Saban primary was not conducted at a Las Vegas hotel but at the Haim Saban Forum at the Brookings Institution in Washington (Saban subsidizes Brookings’ Middle East activities). Held in December 2013 and again last week, Saban featured only one 2016 presidential hopeful this year: Hillary Clinton (Vice President Joseph Biden, who also spoke, will probably not run). Clinton does not have to audition for Saban, because everyone already knows that she is his candidate and that he will be her go-to guy on both Israel issues and funding from pro-Israel donors. He just likes to show her off as his prize catch, the way Adelson paraded Romney around last time.

This is why Adelson and Saban are eager to take their places in the Israel lobby galaxy. AIPAC is not them, and they would like politicians to see their faces when the thought of Israel pops into their heads. Simply put, they want to be the Koch brothers on Israel. And they want to be even more influential than they are, by virtue of having both parties in their pockets and not just one.