In order to increase the amount of relevant details an organism pulls from its sensory data you would need an organism to live in an environment that requires it to know about more details about its environment to survive.
To maximize the details the organism needs you need it to be a predator but not an apex predator. This requires it to use its senses to overcome the hiding techniques of its prey and it requires the organism to monitor its surroundings for incoming threats.
Next you need the organism to be in tune with its surroundings to move. For example, if the area the organism lives in is flat and stable it requires a minimum amount of relevant details to move about in a predictable way. On the other hand, if the organism moves in a volatile medium, say it walks, but on mountains with a lot of seismic activity, it fly's in turbulent winds, or it swims through chaotic currents the organism will need to know a lot more about its environment to safely and precisely move about.
The organism would also require additional knowledge about its surroundings to survive if it used camouflage for multiple senses as its primary means of hunting and staying safe. 802
If the organism camouflages its self visually, it would need to be able to pick out details better than its prey to attack and better than its predators to stay hidden. If it camouflaged its smell it would need to be able to smell better than its prey and its predators as well, etc.
Lastly the organism would need to be warm blooded with a fast metabolism. This increases the energy requirements for the animal and would force it to actively move about which would increase the number of times per day it has to rely on subtle sensory information to survive.
I imagine something like an arboreal shrew that glides between trees like a flying squirrel and has camouflage skin like an octopus. It would need to sense the wind velocity on its skin, the kinesthesic positioning of its body, the velocity of the branch its standing on, the position of the branch it would need to leap to the smell it is trying to duplicate as part of its camouflage, the colors/textures/patterns of the branch it is camouflaging in, all just to determine the right moment to pounce on prey or to flee to another tree.
In an environment that has many effective predators and quick elusive stealthy prey the organism would have to be aware of hundreds of tiny details to avoid death and would definitely have the high "throughput" senses you were looking for. 671