Medaka Box is that new project, and interestingly enough, it isn't so much of an original for GAINAX, but that doesn't mean that they won't find some way to foul it up as soon as they got their hands on it.
Scheduled to air in April of 2012, Medaka Box follows the adventures of Student Council President Medaka Kurokami, and her suggestion box, that she uses to get feedback from the students to help her improve the overall quality of the school, and she works to make them happen, be it finding lost pets, helping attitudes, or fixing up the club rooms.
Everything seems fine until the Student Council discovers a dark secret called Flask Plan, and then of course like everything that GAINAX would work on, it goes into the reals of the bizarre and strange. Nothing ever goes simply, and naturally there are students that have abnormal abilities, there are fights, rival students that want to usurp the current Council, and yadda, yadda, yadda.
You can check out the one minute trailer for the new anime here, but it's mostly just showcasing the look of the characters as they appear in the animated version of the series.
I'm already suspecting this anime to have everything in it that I hate GAINAX for, but that won't stop me from trying it a little when it comes out, to either prove my point, or continue with the love/hate that I feel for them.