Outside of government agencies, many other organizations, both for-profit and not-for-profit, collect (or compile) data. Much of this is public facing and freely available. You may find that some public opinion organizations may only provide initial limited free access to their data.
Look through these to find and build on your demographic research. These include global demographic information, market, and trade specific research.
These institutions typically engage in research focused on policy improvement or change. They regularly publish reports and research and occasionally have publicly available datasets available. You may recognize a few names such as the CATO Institute, the Brookings Institution, or Urban Institute.
Note that many think tanks have a political or ideological bent and their data focuses may reflect that.