"逐店进行搜购" can be translated into English as "conduct a shop-by-shop shopping spree" or "go on a shopping spree from store to store".
"Shop-by-shop" emphasizes the sequential, store-by-store approach.
"Shopping spree" conveys the idea of intensive or enthusiastic shopping.
Alternatively, for a more literal translation that still captures the essence, you could use "search and purchase from store to store" or "shop at each store one by one", though these are slightly less idiomatic in everyday English. The first two suggestions are more natural and commonly used.