Believe it or not, the 11x11x11 Rubik's Cube is an existing NxNxN magic cube. Tony Fisher made a fully functional pillowed cube back in 2009 and now you can play with this puzzle online with this simulator.
According to the Guinness World Records in 2013 the largest order magic cube was 17x17x17, containing 1539 pieces and 1734 stickers. This was made in 2011 by Oskar van Deventer and Claus Wenicker and you can buy one for 1500$. This NxNxN Rubik's Cube has large corner and edge pieces keeping the small inner pieces together, otherwise it would fall apart.
This record was broken in 2018 by Greg's puzzles with a 33x33x3 cube.
The 11x11x11 version is the largest available NxNxN magic puzzle simulator. Just like for the 10x10x10 simulator, the deepest turn is the rotation of 5 layers at the same time. Scramble the 11x11x11 cube and try to solve it using the rotation buttons. Even if you are a speedcuber this operation will keep you busy for a while :)