That's a gorgeous coat. It's going to work well with all your brights, as well as cream. Lovely! I think in this situation I might consider brown footwear or bag and a scarf with some brown in the pattern before going any further down the brown road.
I have added a bit of olive in bottoms-- it's difficult for me, in fact, because I don't have enough tops that work with it, and it isn't good near my face unless it is a very cool, sagey olive. So I might eventually phase it out.
I haven't truly added a new colour to my closet for ages and my wardrobe is almost entirely blue, white, and grey, which does get a bit dull at times. I'd like to increase my reds, berries, and even lilacs.