The point where a theme stops coping
Themes are built and demonstrated on stores with thirty products. At thirty products, a grid and a search box is a complete navigation system, because a shopper can see everything.
A designer fashion store we built for in Mexico runs roughly 972 products. At that size the grid is not navigation, it is a wall. The shopper is not browsing, they are looking for something, and every click between them and it is a chance to leave.
What actually changes
Collections stop being marketing and start being structure. On a small store a collection is a campaign: new in, sale, summer. On a large one it is how a person finds anything, and it has to answer the way people actually ask. Brand, then category, then the thing that matters in that category - size for one, capacity for another.
Filters have to be honest. A filter that returns nothing is worse than no filter. Every facet has to be backed by data on every product, which means the catalogue work comes before the theme work, not after it.
Search becomes a first class screen, not a dropdown. At a thousand products, search is how a meaningful share of buyers navigate. If the results page is the theme's default, that is the page you are least designing and most using.
Performance is a catalogue problem. Collection pages that load every variant, image sets that are not sized, apps that add a script per feature. On a small store none of that is visible. On a large one it is the difference between a page that renders in a second and one that does not.
The apps question
Most large catalogue stores we see have picked up a dozen apps, each solving a real problem and each adding weight and its own opinion about the layout. The twelfth one breaks something the eleven before it had agreed on.
This is usually the moment the owner calls someone. The honest answer is rarely "replace all your apps". It is usually: two of these do the same job, one of them is doing something a custom section would do in a tenth of the weight, and one is genuinely load bearing and should stay.
What to do before you redesign
Look at your own search logs for a week. What are people typing? If the words they use are not the words your collections are named with, that is the redesign, and it costs nothing to find out.
The store this is written from is Premium Avenue. Naming collections after the words people actually search for is where this overlaps with SEO.