I think this is possible; by trying to see how the contents of a situation can THEMSELVES be sufficient to bring about what occurs, or what we are trying to understand. This does not PROVE that what we come up with is independent of our understanding, but in as far as we seem successful there is no evidence it does depend on our understanding.
An example of this is evolution through natural selection, which in turn was influenced by uniformitarianism; the view that the natural world should be explained by the continuation of objects properties and processes currently observable. It is by the continuation of these things that the contents of a situation can seem themselves sufficient.
This in turn gives a different answer to Hume's questions why we suppose the continued (and independent) existence of body; Because, if we can suppose the continued existence of some object as a situation develops, we don't have to draw a conclusion beyond its original existence, so the continuation of that objects original existence must appear sufficient for its part in the development of the situation. For example, if we suppose an object that travels to disappear behind a screen and then re-appears on the other side of the screen; if we can suppose it is the same existence that continues and re-appears, since we don't have to draw a conclusion beyond that original existence, it appears sufficient to account for the subsequent appearance. But if that original existence is to account in this way for the subsequent appearances it must exist behind the screen even in those parts we haven't imagined or thought of.
In this way cause and effect can be made objective sense of insofar as we can avoid drawing conclusions beyond factors in a situation, making the situation a re-arrangement. So, instead of Hume's example of the collision of two billiard balls, we can take an example similar to Archimedes's thinking, that of a ball being pushed into a bucket of water. Since the volume of ball and water continue, as do their other properties (known by experience) such as impermeability of the ball, and fluidity of and weight of the water; as the ball is pushed into the water volume of ball-plus water is more than volume of water alone so the water level rises (and I believe you can see why, if these things continue together in the situation that result should be necessary; no other result is compatible with their continued existence together in the situation). The effect is a re-arrangement, not something essentially new.
Since we are trying to avoid drawing conclusions beyond 'objects' this is different from having to add any description to the situation. So, again, what we are up to is not something obviously added to the situation by us. But of course, it is not the only possible way/attitude towards handing the situation.