I'm not a picking player, but have a lot of respect for those who can do this well (Mike Gordon comes to mind). I create a lot of different sounds with my right hand and move those shapes a lot based on what I want to hear in a given song or solo. I will move between index and middle fingerstyle playing, using thumb index and middle for tighter, more percussive grooves, especially when I use left-hand leading techniques. I will often palm mute when doing this -the heavier that palm mute, the more I can make my electric sound like an upright. I also slap in various styles--sometimes it is that vintage Larry Graham sound I'm going for which has more of a bounce, whereas other times that Victor sound is what I want and so I will use open-hammer plucks and double thumbing. I also like to tap upper extensions of chords while hammering the bass notes in the lower octaves to fill space and add nuance in places. I worked on prettier solo tapping arpeggios and melodies years ago and still can play in that style to a certain extent, but I seldom find times where it is appropriate in the settings I typically play in, so it is a skill that is kind of withering on the vine.
I think the more imaginative you can get in your right hand, the more versatile you can be in a variety of settings - then it comes down to knowing when and where to use these techniques so you can express yourself musically, without being a show-off, or throwing them in just to appear impressive.