To complete your catalogue, you only need to borrow (as opposed to steal) an item from someone. You do not need to purchase it or even take it back to your own town. Just put the item in your pocket for a moment and that will add its entry to your catalogue.

When you visit a friend's town, have him/her place items that are not in your catalogue on the ground. Fill your pocket with items that you have that are missing from his/her catalogue. When you reach the town, empty your pockets and fill them with your friend's items. Afterwards, retrieve your own items and leave your friend's items on the ground for him/her to retrieve. This temporary exchange of items is sufficient to add them to your catalogue.