Flutter is traditionally delayed by modifying either a structure’s geometry or its stiffness distribution. Here, we show that allowing both to evolve simultaneously can unlock a fundamentally different route to aeroelastic stability. We concurrently optimize the cross-sectional geometry and fiber paths of a composite thin-walled wing–engine system to maximize flutter onset. The wing structure is modeled using Classical Laminated Plate Theory, while unsteady aerodynamic loads are represented by a Mach-number-corrected Wagner state-space formulation. The engine is modeled as a lumped mass with rotational inertia, follower thrust, and its associated gyroscopic reaction. The wing cross-section is parameterized as an arbitrary smooth closed curve, while fiber orientation is independently varied throughout the wing structure. A continuous penalty formulation prevents pinching, self-intersection, and excessive curvature during optimization. The optimization employs a modified Parallelized Complex Method (PCM) originally proposed by Namani Koureh et al. (2026) for fiber path optimization, reformulated here to accommodate variable cross-sectional geometry. The optimized designs achieve an approximately 42% increase in flutter speed relative to fiber-only optimization. Notably, this improvement does not result from suppressing the conventional flapwise flutter mechanism. Instead, simultaneous geometry–fiber tailoring fundamentally alters the aeroelastic instability pathway, with flutter onset becoming governed by a chordwise mode. These results demonstrate that concurrent optimization of structural geometry and fiber paths can redirect aeroelastic instability toward an alternative mode in thin-walled wing-engine systems.