I don't care for the brown as the alternate squares. I think any color that is already represented in the blocks would look fine, like the lilac, green, rose, yellow, or black. I would use whichever color you want to emphasize, because whatever color you use for the alternate squares, it will dominate, and the quilt will become a "lilac" quilt, or a "black" quilt, etc.
Very attractive blocks, btw!