I ran a short story arc that was publicly posted on the IGS about this, actually. I checked with Falcon and he gave me a thumbs up to go ahead and do it (though assured me he and CCP will not validate any of it).
What I had imagined was that the CEP is actually much much larger than we tend to think it is. The Big Eight are the major decision makers, but there are also CEOs of smaller corporations present at the Panel. Not all of them will get a seat at the fancy round table, likely. Or maybe it's a speaking chamber more like the Senate or Parliament. At any rate, I imagined that assuming you fill certain criteria, you can get a seat as CEO of a State corporation - even if you're not directly under the Big Eight.
Kat's corporation "Oniseki Holdings" applied to become a valid State corporation and get a seat. Eventually they were approved, and were renamed "Oniseki Corporation", but the price she had to pay was that Katrina had to relinquish her chair as CEO and become a majority shareholder only. I figured CEP and CCP would not want a capsuleer sitting on the CEP. Of course... none of this is anything anybody has to recognize IC or OOC... but it was fun for me to do. It'a also one of the reasons you rarely see her talking about it these days, since she no longer controls it.
Anyways...
I think there may be varying levels of the CEP. There may be the primary "Big Panel" comprised of the eight CEOs of the megacorps, who get all the real power of the CEP and media attention. Then you have a "Small Panel", perhaps comprised of non-mega CEOs mega-subsidiary CEOs. Of course, the larger and more powerful one of the Big 8 is, the more influence and direct power they will have over these independents. It may be a very real political game where the battle is over how many Small Panel seats the Big Panel can control and/or influence. Think of it as top-down lobbying and bribes.
Lai Dai and CBD might be fighting over a legislative bill. Lai Dai has far more money than CBD, but CBD has more subsidiaries sitting on the Small Panel. You can imagine a bitter political war being fought between the two as CBD tries to keep its own Small CEOs voting in favor of its preferences, while Lai Dai is trying to pay them off to vote temporarily in their favor. The battle might extend further as CBD and Lai Dai both try to influence their allies and other parties to vote for them as well.
Big Panel - the Big 8 CEOs who get all the media coverage and have the real deciding power.
Small Panel - All the other independent CEOs who are likely all paid off, controlled, and juggled by the Big 8.