A two-species predator-prey system of Lotka-Volterra type that includes harvesting terms, can have four equilibria in the positive quadrant. In this paper, it is assumed that all the parameters of such a system are positive

$p$-periodic continuous functions. The authors make use of Mawhinâ€™s continuation theorem of coincidence degree theory to prove that, under certain inequality assumptions on the periodic parameters, there exist (at least) four

$p$-periodic solutions of the given system. Finally, a numerical example of such a system is presented that satisfies all the assumptions of the theorem.