I have built and worked under hot rods and race cars for years under jack stands. If you just need to get it up enough to get under it, just jack one side at a time as mentioned above. If you really need to get it up in the air to pull a transmission or something like that, do it in stages. Jack one side up part way and place jack stands. Then, jack the other side up level. Make sure everything is stable and repeat to the higher level. Following the same procedure when lowering it.
As far as stability, if your jacks stands are placed evenly on secure lift points and on a flat surface, the car should not move at all. It is no different than being on the four little pads of a life.