  If $X$ is an infinite-dimensional uniform algebra, if $X$ has the Daugavet
property or if $X$ is a proper $M$-embedded space, every relatively weakly open
subset of the unit ball of the Banach space $X$ is known to have diameter 2,
i.e., $X$ has the diameter 2 property. We prove that in these three cases even
every finite convex combination of relatively weakly open subsets of the unit
ball have diameter 2. Further, we identify new examples of spaces with the
diameter 2 property outside the formerly known cases; in particular we observe
that forming $\ell_p$-sums of diameter 2 spaces does not ruin diameter 2
structure.
