It appears you're wanting the two competing frequency sharing instruments (vocal and piano in your example) to set together better in the overall mix. Although you're correct that the two will share much of the frequency range and the amount they share at any one time is going to be constantly shifting, it's the range that's critical to achieve a better mix between the two instruments.

Using the Piano and Vocal example, cut a range of frequencies shared by both instruments on one instrument and boost those same frequencies on the other. Since vocals are king of a mix, I'd cut the piano and boost the vocals. You are simply carving out some space to give the vocals free space to sit into the mix and reducing competition. Done correctly and sparsely, you don't really hear it. The vocals just clearly cut through the overall mix. It's a common technique.

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