Grid-shaped and tree-shaped flow architectures are being generated for use in vascularized materials with multiple functionality (self-healing, self-cooling, etc), based on the principle of the constructal law of evolutionary increase of flow access through the generation of better flowing configurations (designs). Here we investigate systematically the advantages of endowing the complex flow architecture with more freedom to morph. Four ways to increase design freedom are explored: multi-scale grids (one, two, three and four diameter sizes), multi-shape loops (square, triangular, hexagonal, rhombic), multi-shape bodies (hexagonal, square, rhombic) and vascularization with grids versus trees. We show that significant gains in global flow access are achieved as the number of optimized channel diameters increases. The most promising combinations of body and loop shapes are hexagonal bodies with triangular loops and square bodies with square loops. The tree-shaped architecture outperforms the grid, but it is recommendable only for stressed bodies in which the most likely location of the cracks is known ahead of time. The effect of body size on the global performance of vascularized multi-scale and multi-shape materials is documented. Diminishing returns and increasing robustness set in as the complexity of the optimized flow architectures increases.