Big projects, like the one you were describing earlier, may be broken up into various pieces, with different students focusing on specific tidbits that are big enough to fit into the thesis scheme of whatever university that is.
If you already have a rapport and have already started, and like that professor as a major professor, and his lab can take you in once you graduate, and you like them, then while it is important to also research around for other options, I don’t think it is a bad idea to continue.
