There is something a bit contradictory in saying that there is a level above us that we are not aware of, but by taking drugs we can become aware of it. If it's a separate layer than ours, how can we move towards it while remaining ourselves? And why can't we go lower, and become aware of the consciousness of our organs or cells?
The way I see it, our consciousness is like a hot air balloon, always floating upwards, but our brain (specifically the ego) tethers it to the here and now, so that we can survive in the physical world. What psychedelic drugs do is loosen the rope, weaken the ego, and let us float higher. If you get high enough, you experience "ego death", which in this metaphor just means that you can't see the ground anymore.
(in contrast, some drugs, like cocaine, make the ego even stronger)