Morphing aircraft, which adapt their aerodynamic shape online to meet mission demands, are a prominent research topic for maintaining high performance across wide flight envelopes. To address the challenges of integrated coordination between online/offline design variables and multi-profile heterogeneous constraints in the aerodynamic design of morphing aircraft, we develop a multi-mission aerodynamic design method for cross-domain aircraft. The proposed method parameterizes the aerodynamic shape with both online and offline variables and constructs an inner-outer dual-layer coupled optimization framework aimed at achieving a globally optimal offline shape while meeting the optimal online configurations for each flight profile. The method was applied to a variable-sweep cross-domain aircraft, and shape optimization is carried out for take-off/landing (max lift coefficient) and high-speed flight (max lift-to-drag ratio with center of pressure constraints). Depending on the objective weights, the optimized lift coefficient at Ma=0.4 increased by 55.03% and 56.85%, while lift-to-drag ratios at Ma=6.0 and Ma=10.0 increased by 1.16%, 1.69% and 0.94%, 1.68%, respectively. Crucially, the high-speed center of pressure variation was successfully controlled within the 2% design constraint in all cases. These results verify the effectiveness of the proposed optimization framework.