"Of course we can. You'll need to scare up some clothing that at least appears close to matching the period so there won't be too many questions, though honestly we could simply buy some clothing on the other side of the door. It opens just off the Khan el-Khalili and we can find just about anything there is to buy there. Any women going through the door will need to be covered up beforehand, but men's suits haven't changed enough to be immediately spotted as different."