A multi-component stent-graft system includes a first stent-graft, and second, third, and fourth branching stent-grafts. The first stent-graft is shaped so as to define, when in a radially-expanded state, proximal and distal superior first lateral openings facing in a first radial direction, and a distal inferior first lateral opening facing a second radial direction generally opposite the first radial direction. The second, third, and fourth branching stent-grafts are configured assume radially-expanded states, wherein the first, the second, the third, and the fourth stent-grafts are configured such that the branching stent-grafts form respective blood-impervious seals with the first stent-graft around the distal inferior first lateral opening, the distal superior first lateral opening, and the proximal superior first lateral opening, respectively, when the branching stent-grafts are disposed therethrough, respectively, and the first, the second, the third, and the fourth stent-grafts are in their radially-expanded states.