To answer with a sequence of increasingly "systemic" ideas (naturally the following will be tinged by by own political beliefs about what's tractable or desirable):
There are lots of object-level lobbying groups that have strong EA endorsement. This includes organizations advocating for better pandemic preparedness (Guarding Against Pandemics), better climate policy (like CATF and others recommended by Giving Green), or beneficial policies in third-world countries like salt iodization or lead paint elimination.
Some EAs are also sympathetic to the "progress studies" movement and to the modern neoliberal movement connected to the Progressive Policy Institute and the Niskasen Center (which are both tax-deductible nonprofit think-tanks). This often includes enthusiasm for denser ("yimby") housing construction, reforming how science funding and academia work in order to speed up scientific progress (such as advocated by New Science), increasing high-skill immigration, and having good monetary policy. All of those cause areas appear on Open Philanthropy's list of "U.S. Policy Focus Areas".
Naturally, there are many ways to advocate for the above causes -- some are more object-level (like fighting to get an individual city to improve its zoning policy), while others are more systemic (like exploring the feasibility of "Georgism", a totally different way of valuing and taxing land which might do a lot to promote efficient land use and encourage fairer, faster economic development).
One big point of hesitancy is that, while some EAs have a general affinity for these cause areas, in many areas I've never heard any particular standout charities being recommended as super-effective in the EA sense... for example, some EAs might feel that we should do monetary policy via "nominal GDP targeting" rather than inflation-rate targeting, but I've never heard anyone recommend that I donate to some specific NGDP-targeting advocacy organization.
I wish there were more places like Center for Election Science, living purely on the meta level and trying to experiment with different ways of organizing people and designing democratic institutions to produce better outcomes. Personally, I'm excited about Charter Cities Institute and the potential for new cities to experiment with new policies and institutions, ideally putting competitive pressure on existing countries to better serve their citizens. As far as I know, there aren't any big organizations devoted to advocating for adopting prediction markets in more places, or adopting quadratic public goods funding, but I think those are some of the most promising areas for really big systemic change.
I enjoyed reading your comment and the links you shared. I learned a lot, thank you. I found charter cities and New Science especially interesting since I'd never heard of those areas before.
I think the absence of other nonprofits focused on systemic change encourages me to love CES even more (I understand there may be some nonprofit neither of us have thought about, but it's encouraging to hear from someone more educated in the space that there isn't some big obvious one that I hadn't considered).