There's usually a few general rules for filling up the sound, and it's often NOT about playing chords, busy bass lines, synth pedals or any of that. If a solo guitarist, a good drummer, or even some killer bassist like Michael Manring can do it with basic, not at all fancy equipment, so can even the most mediocre of trios. Combined, y'all have way more versatility then anyone playing solo. So, IMHO, it always goes back to dynamics, technique, listening to everyone, everyone else listening to everyone else, and good feel.
Here's how to start on the right path:
1. Play distinctly, filling up your space sonically well.
2. Get everyone else (drummer, keys or guitar) to play distinctly, too, but not stepping on the other distinctly played parts (including the vocals).
3. Don't overplay. Less really is more, usually, with all the instruments (and sometimes vocals).
A great example of those is in Primus's "Tommy the Cat." - Every note Mr. Claypool plays is very, very distinct and accurate, and he's hitting them hard to pull some big notes out of them. During the verses, he even stops playing in Tommy the Cat and only three 16th notes at the start of the bars in "Harold of the Rocks." In fact, during the verses, there's pretty much only drums, yet the sound is full because the drummer is rockin' it, and playing very distinctly and drawing a whole lot of tone out of those drums.
As a whole, both of these songs, as well as almost any trio's songs, are very, very dynamic. There are parts where there are breaks where there is literally no sound coming out of anyone's instruments, even the drummer.
As Salcot mentioned, listen to the Police. That's a great example... simple bass lines with lots of space in them. Same with the other guys in the band. Then there's Rush or King's X, or other Primus songs. There's tons of others out there in almost any genre. Listen to other trios (and four-pieces that have a singer that doesn't play anything), and figure out what they're doing, how they're interacting with the drummer and everyone else in the band. Also, you can look at some funk bands... While they might have 10 guys on stage, most of the time, they're playing nothing or very minimally so that all you really hear is bass and drums.
Sometimes, it is about getting a synth pedal or an 8-string bass, but the truth is that it rarely really needs any of that. 99% of the time, if you have good technique and are versatile, you can usually pick out a good bass line that'll fill up the space.