For example, shopping habits on the web site can show buying patterns and trends that could translate to the brick and mortar store. Looking at what people search for together online could give a clue to what they are looking for when they get to a store.
Note that the could in the previous observation is very much an imponderable. While the shearing "Stuff" on the web site is really easy (facilitating A/B testing, for example), it is still tricky in the brick and mortar store.
Reorganizing store shelves/layout runs the risk of confusing staff and customers. Things aren't where they were yesterday. Our ingrained habits and expectations no longer work for us. So the risk is definitely there, but there could be some interesting small experiments.
Perhaps it is worth grouping trousers by style/size and not by color. Perhaps it is worth grouping shoes by size, mixing up the brands. Of course that one is very tricky because we buy shoes with our eyes, so we may need to see a floor sample which will be of a single size.
The desires of the store, the desires of the brands and the desires of the customer may well come into opposition.
The online shopping experience can give us a rate of change greater than that in the physical store - delivering data to the store planners and merchandisers that can influence product placement - and the ultimate goal of selling more "Stuff" to the customers