You could play an extended game of Room 101 . Before you set off, each player makes a secret list of, say, six things they would like to be wiped from existence, never to be seen or heard of again. These ‘things’ can be people, places, trends, fashions, styles of music, certain foods, institutions, professions, aspects of technology… literally, anything you want to nominate. Players take it in turns to nominate something from their list to be banished to Room 101 forever. One player is the Keeper of Room 101 and gets to decide whether the nomination has merit or not.
The player can argue his or her case, the Keeper gets to play ‘devil’s advocate’ and question the reasoning, and everyone else is free to weigh in with opinions, either supporting the nomination or saying why it should be rejected. The Keeper’s decision is final and binding, and you really need someone to play this role with a degree of impartial fairness for the game to work.
A player gets one point for each successful nomination. The aim of the game is to get more points than anyone else. A very important additional rule is this: the order of play is decided randomly at the start. if anyone mentions one of your nominations before you do, you lose that item from your list and you can’t replace it, thus you have fewer chances to win. This places the onus on each player, when devising their original list of six items, to come up with items that (a) are very likely to successfully get banished to Room 101, yet (b) no-one else will think of. The difficulty of thinking up such items gives the game its richness. Remember, people can take days preparing their list if you announce the game sufficiently far in advance.
It fits the OP in the sense that playing the game is equivalent to asking lots of very diverse questions about pet likes and dislikes, favourites and least favourites and so on.