Setting the bevel is the thing. That's all the heavy lifting done at that point. You cannot progress without this having been done right.
The rest of the progression is about refining and polishing that edge so that it doesn't just cut, but does so comfortably.
To answer your question - yes, you can do exactly the same strokes on the next stone, (and that's ideal - less to worry about) but typically the pressure is lightened as the edge becomes more fragile.
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