"Have you been to this shop?"
你去过这家商店吗？（Go or Come) to have Been? Came or Gone?
你来过这家商店吗， Have you been to THIS shop?
你去过那家商店吗， Have you been to THAT shop?
Direction of movement in relation to the speaker means that 来 should be used here..
I would assume that you mean other possible ways of saying.
Of course, there are other possible sentences, which depend on the context. Here is the list:
- 你去過這個商店嗎？(個 is the most used classifier if you are not sure of which correct one to use)
- 你去過這家商店嗎？(Most accurate sentence, using 家 as the classifier)
The sentence refers to "this shop", which suggests the speaker is there at the shop.. Therefore you should use "come, 来" rather than "go, 去" to describe a journey to the place.
If you wanted to use 去， the question 你去过那家商店吗, "have you been to THAT shop?" would be correct.
The word 来 is mistranslated like been, it should be come, I wait responses.