I've discovered an easy way to work your way up the celebrity ladder for those who don't mind buying their fame (and have the money for it, of course): Donating household items to fans! Simply click on something and select Donate, and the more it's worth, the more fame you will earn. My comedian donated a computer worth 10,000 §, and the impact it made on the fame bar was the biggest I've seen so far! Very useful for getting rid of unwanted career rewards and other stuff in the household inventory - granted, you could also just sell it, but you get it for free, so you might as well give it away for free and earn a better celebrity status.
The downside is that you can only do this once you have 3 or 4 stars, and it doesn't work with purely decorative objects, but things like computers, gym equipment and even toilets are fair game. Occasionally you might also get a call asking for a donation of 1,000 §, which you can accept. Thanks to this (and, of course, social media, the drone, and almost daily public performances), my comedian has finally completed the World-Famous Celebrity aspiration and even received an accolade. :)