There is an outdated wiki and of course discord.
The princess scepter can be found by sitting on the throne. With a lot of luck, no headgar equiped and no item in your hands.
If you already have the class and are missing items, you can summon them in the mansion. There is a wardrobe that will summon missing class items that might not have spawned due to clothing restrictions.
You do not need the scepter but it makes it easier to fulfill the quest because it directs you to where the activites are. Be friendly to the guards, visit the cage, remove the tentacle spawner, visit the shop, go upstairs.
I think you miss most classes by already having a class. The obvious classes are by items you pick up while not having a class. But there are many classes you obtain by doing activities in certain circumstances. I think the most easy would be cheerleader. Easy to obtain and easy to miss. Just let your hair grow very long. It gets complicated because there are many classes that can crossclass and to obtain the crossclass there might be different routes not being the same as obtaining the other base class. As far as I know you cannot get a cheerleader cross by growing your hair while having another class.
Things to try (while not having a class): crawling a lot on the floor. Cleaning puddles. Dominate enemies. Seducing an npc to the finish. Praying on the altar. Dipping drinking glasses in containers.