Currently, 'Personalize results' has block, lower, normal, raise and pin.
But stores are kind of a funny thing... I don't want them cluttering up my results normally, but when I'm shopping, they're actually what I'm trying to search for.
Thus, a special category/checkbox for 'Store' for personalizing results would be nice. A site marked 'store' would effectively be a ban, unless the user is using a new lens (or main category) for 'Shopping', at which point their regular 'personalize results' for the site would apply.
Alongside the current options (ban/lower/normal/raise/pin) would be a new checkbox to mark a site as a store. That site would then normally be omitted from search results, like 'ban'.
However, when the user selected the appropriate lens for 'Shopping', the ban would be removed, allowing stores to appear in the search results.
There is no browser feature or similar feature in other search engines that I am aware of.