This paper investigates the sum-capacity of two-user optical intensity multiple access channels with per-user peak- or/and average-intensity constraints. By leveraging tools from the decomposition of certain maxentropic distributions, we derive several lower bounds on the sum-capacity. In the high signal-to-noise ratio (SNR) regime, some bounds asymptotically match or approach the sum-capacity, thus closing or reducing the existing gaps to the high-SNR asymptotic sum-capacity. At moderate SNR, some bounds are also fairly close to the sum-capacity.