This application relates to methods, systems, and apparatus for replacing native heart valves with prosthetic heart valves and treating valvular insufficiency. In a representative embodiment, a support frame configured to be implanted in a heart valve comprises a main body formed by formed by a plurality of inner members forming an inner clover and a plurality of outer members forming an outer clover. The support frame can include gaps located between inner members of the plurality of inner members and outer members of the plurality of outer members. The inner clover can be radially inside the outer clover, and the outer clover can have larger dimensions than the inner clover. The support frames herein can be radially expandable and collapsible.