You can alter the colours available via Ctrl+K, by using Alt+K first.
By doing that, you can pick and choose what 16 colours you want showing in Ctrl+K, and (I think) that brings it up to a possible range of 16384 colours.
Note: that if you change the colours using Alt+K, the items that used the old colour will now use the new one, so that at any one point, you still only have 16 colours available to pick from using the Ctrl+K dialog.
Extended colours have been suggested before.
