Eq and panning is one way.
A couple of weeks ago the interview about mixing was here somewhere. The guy said something like: "When the bass starts a solo, software just dims the bass drum for that sequence so that the bass has more room." I will lok for that thread...
When I sing to playback tracks, those are eq'd to give room to my bariton voice.

Another way is arranging.
I play rhythm guitar. When I accompany myself I mostly play barré chords. when I play with a band I must not use those chords. These chords often just double notes, like the root note is played two or three times in different octave. The guitar plays a lot of notes the piano is playing or plays the same notes as the bass does. It may interfere with the singer in his/her vocal range. Freddy Green, google him if you want ton know more, in his later years used to play rhythm guitar using "single note chords".
When I accompany myself, this way of playing would sound awfully thin.

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