In this paper, the authors investigate a majorization problem for certain subclasses of multiva-lent meromorphic functions defined in the punctured unit disk U * having a pole of order p at origin. The subclasses under investigation are defined through iterations and combinations of the Liu-Srivastava operator and a meromorphic analogue of the Cho-Kwon-Srivastava operator for normalized analytic function. Several consequences of the main results in form of corollaries are also pointed out.