I forgot exactly how Madrid built their extensions, but it had an interesting clause or so - basically all profits of the extension (or line depending on how much was built by the private sector) would go to the company, however, the company also assumes all risk. No profit - no money for the company. Although the built form of the city above is drastically different than where Sheppard is going...
This model would work great if the line they were building with PPP were actually profitable. There's no way Sheppard is going to be profitable, hence why no business in their right mind would agree to any deal unless they were guaranteed their investment back (no risk). Which, in that case, the City just might as well finance it through a loan, as it would probably be cheaper than what the private company would want as ROI.