Technologies are shown for self-elevating platform carts that can transport a load from an initial surface to a destination surface that can be at a higher level, lower level or same level across a horizontal distance and/or barrier. One example extends a front height support to contact the destination surface and extends a rear height support control to contact the initial surface. A main lift is retracted and the system moved forward until main wheels on the main lift contact the destination surface. The main lift is extended and the extensible support beams and height supports are retracted. Another example traverses intermediate surfaces using a vertical stabilizer to stabilize the main lift on surfaces at different levels. The main lift can be the only power lift for the cart.