Rooms in common with another member
It is useful to be able to fetch rooms you have in common with another user. Popular messaging services such as Telegram offer users the ability to show "groups in common", which allows users to determine what they have in common before participating in conversation.
… or also to find the most appropriate room to have a specific conversation with someone. This would belong on the room member profile.
MSC2666 is still in Final Comment Period, but this can be done locally until it gets in the spec and implemented by home servers.