A palette of six equal colours is a palette of none. The brands people recognise by colour alone use one, and they are strict about where it goes.
Assign the job
Decide what the brand colour is for: the action, the highlight, the one word in the headline. Everything else is neutral, black, white, grey. The colour then means something every time it appears, because it appears for a reason.
Check it holds up
- Look at a page with the colour removed. It should still work, just quieter.
- Look at a page with the colour on everything. That is what you are avoiding.
- Test the colour on text for contrast; a brand colour that cannot be read is a logo colour, not a system.