We study the capacity region of distributed index coding in a multiple unicast setting. In contrast to the traditional centralized index coding where a single server contains all $n$ messages, in the distributed index coding model there are $2^n − 1$ servers, each containing a unique non-empty subset $J$ of the messages. We first enhance an existing composite coding scheme for the centralized index coding problem, which is then merged with fractional partitioning of servers to yield a new coding scheme for distributed index coding and an associated inner bound on its capacity region. We also establish a new outer bound on the sum capacity of distributed index coding. These results lead us to establishing the sum capacity for almost all (213 of 218) non-isomorphic index coding problems with $n=4$ messages.