Another problem with this plan (assuming you get past Rocky's answer somehow) is that you assume that $50K in construction costs will translate to $50K in increased value. That's not always true; the ROI on home improvements is usually a lot less than 100%. You'd also owe more property taxes on your improvements, which would cut into your plan somewhat.
But you also can't keep doing this forever. Soon enough, you'd run out of physical and/or legal space to keep adding additions to the house (zoning tends to limit how much you can build, unless you're in the middle of nowhere, and eventually you'd fill the lot), even if you did manage to keep obtaining more and more loans. And you'd quickly reach the point of diminishing returns on your expansions. Many homebuyers might be prepared to pay more for a third or fourth bedroom, but vanishingly few in most markets will pay substantially more for a second billiards room or a third home theater. At some point, your house isn't a mansion, it's "that ridiculous castle" only an eccentric would want, and the pool of potential buyers (and the price they'll pay for it) diminishes.
And the lender, not being stupid, isn't going to go on financing your creation of a monstrosity, because they are the ones who will be stuck with the place if you default.