How big can a WooCommerce store be?

The folks at MarketPress did a poll to see how big of shops people have built and managed with WooCommerce. 29% of respondents said they'd built a shop with 250-1000 products, and 11% said they'd built one with “1000+” products. It's an interesting poll, but I see two problems. First, fewer than 40 people responded. And second, they really need more options at the “1000+” level. I fit into that category with a few projects, and I can tell you there would be a huge difference in complexity managing and scaling stores with 1000 products, 3000 products, 10000 products, or 50000 products.

I'm interested to know in the comments if any of you have built stores with more than 1000 products, and the details of just how big and how well it scaled would be great information if you're willing to share.