Unfortunately, there is no way to really edit or save styles on the PSR-E473/EW425. The closest feature they have is the ability to change the voices of the style tracks, and then those new settings can be saved to a registration. But you cannot actually create or edit the details of a style, such as changing the rhythm of the drums, background melodies, or pads, or by adding new style tracks, onboard these keyboards. However, you CAN load external styles from other sources, including (as far as I know -- I've never done this personally) styles found on this site.
If these newer keyboards are similar to the previous versions of the E/EW400 series models, then the general limitations are that the styles cannot be more than about 50k-bytes in size, and they can only have two variations. I think if you try to load a style with 4 variations, like what can be played on the higher-end PSR-S/SX models, then only variations A and B will work.