All styles can be played by the psr 670.
It can play better the styles that were made on models like the s750-950-650-770-970-775-975
because most of the drumkits and voices are identical but it can also play all styles from tyros line and genos.
BUT you have to adjust or equalize or replace the voices that don't sound nicely because the keyboard doesn't have those voices or they are styles that made on older keyboards and they need a "refreshment" with the newer voices of the s670.
Many of us use the on board Mixing console to adjust the styles to our liking.
For example I took 2 different older styles and combine their best parts to make a newer style
like this:
https://soundcloud.com/user-74537650/conquest-of-paradise-coveryamaha-psr-s750-keyboardor getting the converted Genos' style for the Tyros 5 and equalized it to play this one:
https://soundcloud.com/user-74537650/game-of-thrones-main-themeyamaha-psr-s750-keyboard-coveror the style someone uploaded recently for "Sadness" by Enigma in the style area,for using on a Genos, sounds just perfect on my older keyboard too.
Don't mind about the poor audio quality it's because I have used the on board recording with settings to suit to my keyboard's headphones(I prefer flat equalizer not to harm my ears by using the headphones all the time;D)
and not recording with an external device for much better sound quality.
On my keyboard they sound just fine.
Probably you won't find a cover that even when I used a preset style I haven't changed something to it to suit to my liking and the song.
Visit a shop and just play a little with an s670 to see how it sounds.