There are many synonyms for the phrase "shop with," depending on the context. If you want to say that you went shopping with someone, you could use words like accompany, go with, or tag along with. If you want to talk about the act of shopping, some alternatives to "shop with" include browse, peruse, and hunt for. To emphasize the social aspect of shopping, you might say that you "chatted with" or "spent time with" someone while shopping. Overall, there are plenty of ways to express the idea of shopping with someone or alone, depending on the nuance you want to convey.