Hey there, ldeliz,
Thanks so much for using Apple Support Communities. We want to help you get ready for your party with some great music.
To answer your question, there isn't currently a way to add multiple genres or artists to a radio station, as it simply works off of the initial artist or genre you started it with. There also isn't a way to necessarily shuffle radio stations, since they are generated each time you play that station as opposed to a set playlist of songs.
We do have an idea that may work for your needs, however. If you have an idea of the music you'd like to use for your party, you could use the curated playlists built into Apple Music to curate your music. This would basically let you pick any genre in Apple Music, find a great curated playlist or two and add them to your library. From there, you could simply shuffle those playlists anytime. You could even combine multiple playlists, creating a larger multi-genre playlist that combines all of your favorites.
This article has more information on how to do all this: Find new music with Apple Music on iPhone - Apple Support
We hope this does the trick for you!
Cheers.