Fiber-reinforced composites have become the primary option in various lightweight applications due to their superior mechanical properties, cost-effectiveness, and adaptability. Late advancements in additive manufacturing technologies have enabled the fabrication of variable stiffness composites that involve curvilinear fibers. Accordingly, various design methodologies have been proposed to determine optimal structural topology and fiber directions in different scenarios. However, combined optimization of the variables controlling geometry and anisotropy can induce local optimality problems due to the initial fiber angles' influence on the solution and the high dimensionality of the corresponding design space. To overcome these pitfalls, we propose a collaborative strategy that iteratively optimizes structural topology and fiber orientations. Our method reduces the number of design variables via sparse anisotropy control parameters assigned to the nodes of coarse auxiliary meshes, which are adaptively generated over the solid region. In addition, to alleviate the design sensitivity to the starting fiber direction field, the fiber volume fraction is progressively increased from an isotropic state. In static problems, the developed scheme was shown to generate designs that exhibit higher structural performance than the ones attained using the conventional concurrent optimization approach. In this paper, we extend our technique to multi-objective optimization problems, where minimum compliance and maximum fundamental eigenfrequency are targeted. Since the chosen objectives require different designs, a set of non-dominated solutions is obtained using different weights for the normalized responses. The case studies demonstrate that the proposed method can produce lightweight composite structures with improved static and dynamic attributes, while exhibiting robustness against changes in the initial fiber orientations.