Existing technique on domain adaptive person search commonly utilizes the unified framework for jointly localizing and identifying the person across domains. This framework, however, inevitably results in the gradient conflict problem, particularly in cross-domain scenarios with contradictory objectives, as the unified framework employs shared parameters to simultaneously address person detection and re-identification tasks across the domains. To overcome this, we present a novel mixture of submodules framework, dubbed MoS, that dynamically modulates the combination of submodules depending on the specific task to perform person detection and re-identification, separately. We further design the mixtures of submodules that vary depending on the domain, enabling domain-specific knowledge transfer. Especially, we decompose the main model into several submodules and employ diverse mixtures of submodules that vary depending on the tasks and domains through the conditional routing policy. In addition, we also present counterpart domain sample generation that synthesizes the augmented sample and uses them to learn domain invariant representation for person re-identification through the contrastive domain alignment. We conduct experiments to demonstrate the effectiveness of our MoS over the existing domain adaptive person search method and provide ablation studies.