Colour Palette Troubles

This colour palette is for a web app (under NDA.) I've been working with it for a couple of months. The app's primary audience is female, aged between 18-35 and fairly tech-savvy.

Generally the client and I are pleased with the blue colours, but lately the greys (even though I've tried to give a warmth to them) come across as slightly corporate and even a bit retro (like the colour of old PC plastic...)

Anyway, if anybody has any ideas on subtle colours I could use to warm up this palette, I'd really appreciate any opinions!