it's certainly possible that private money funds this, but highly doubtful. why? because it's mostly a money-pit operation. investors have an almost zero chance of getting a return on their money in their own lifetime. spaceX is mainly competing for gov't money either in the form of seed money for R&D or as their main customer for LEO trips.

don't get me wrong, I love SpaceX (and Elon), but most of this is folly.

Even terraforming Mars isn't realistic, it's a mostly dead planet whose core has cooled and now doesn't have any protective electromagnetic belts.