A stabilizing support system for a body-gripping trap is disclosed. The stabilizing support system comprises a trap-engaging apparatus for removably engaging a body-gripping trap, and the trap-engaging apparatus comprises a pair of jaw engaging members for engaging opposite jaws of a trap. Each of the jaw engaging members comprises an upper portion and a lower portion, with the upper portion comprising a pair of laterally-spaced arms and a bridge joining the pair of arms, and the lower portion comprising a pair of laterally spaced legs. The apparatus also includes connectors for connecting the pair of jaw engaging members together in an opposed orientation.