Yes. There is a vent a hood within our wood hood.

That's what I am planning to do. Most wood hoods have vent inserts. Braun is a popular choice, but I ordered XO brand. It has a Stainless filter rack that you can take out and wash. I believe some models have fiber filters that have to be replaced on occassion. I didn't install mine yet, so I am not sure how well it works. Hopefully, you will get some response from those who actually have a vent insert.

Aesthetics aside, 30 inches from stove top (not from top of grills) to vent hood bottom is the minimum height typically advised for the bottom of the mounted vent hood. Vent hood height may be higher if your range/cooktop manufacturer stipulates so and you plan to avail yourself of the warranty.

Wood mounted over stainless brings a new considerations into play: stainless is far less combustible than wood. Height matters. Two vent hood surfaces, one slightly higher, yet close to the lower vent hood, may result in a non-vented grease pocket on the wood vent undersurface, require nimble fingers to clean if even possible, and pose a fire hazard which is why the motor system is a main component of the kitchen ventilation system. One other thought is weight limit on your back wall mounting surface with two hoods, as that's a lot of weight on the back wall.

It's good to ask and do your research first. Hope this helps.

Ah, perhaps I misunderstood your post as mounting a new larger wood hood over a pre-existing, primary ducted, and probably stainless vent hood. If so, please excuse.