A shopper sees "You can compare up to 4 products". Can they compare more?

That message means the shopper reached your limit. The default is 4. To raise it, go to Products → Product Comparison and set Max products compared at once to anything from 2 to 6, then click Save.

Shoppers can also remove a product from their compare list to make room for another. Keep in mind that a wide table is harder to read on a phone, so 3 or 4 is often easier for mobile shoppers.