Embodiments of the present disclosure include an implantable assembly for a native heart valve that includes a prosthetic heart valve and a braided support structure. The prosthetic valve includes a frame and prosthetic leaflets. The braided support structure has an inner braided layer and an outer braided layer. The outer braided layer is disposed over the inner braided layer. The outer braided layer is less porous to blood than the inner braided layer. The braided support structure defines a plurality of arms that are angularly spaced around the prosthetic heart valve such that each arm extends radially outwardly from the prosthetic heart valve. Other embodiments are also described.