Part writing?

I have a question regarding part writing. Let me explain.

When I have my chord progression written. The norm for me is to use the top line, middle line, and bass line as my lines for various instruments. However, I've been experimenting with using the root, 3rd and 5th as separate lines for my instruments instead which has instruments overlapping each other melodically due to chordal inversions. What are the rules on doing this, if any? Thanks in advance for any help.

Seems like more of a harmony question.

If you have a strong bass line and good independent voice leading, what the instruments play will naturally follow.

"Rules"

Well, it depends what you want. Seems you are having trouble with voice crossings and too close voicings. This requires another questions: How much harmony and counterpoint have you studied? What type of music have you written before? The voicings you'd use for pop music versus a good deal of classical music differs.