This paper sketch the method of studying the Multiplier Conjecture that we presented in [1], and add one lemma. Applying this method we obtain some partial solutions for it: in the case n = 2n(1), the Second Multiplier Theorem holds without the assumption ''n(1) > lambda'', except that one case is yet undecided where n(1) is odd and 7\\v and t = 3, 5, or 6 (mod 7), and, for every prime divisor p(not equal 7) of v such that the order w of 2 mod p satisfies that 2\phi(p)/w; in the case n = 3n(1) and (v,3 . 11) = 1, then the Second Multiplier Theorem holds without the assumption ''n(1) > lambda'', except that one case is yet undecided where n(1) can not divide by 3 and 13\\v and the order of t mod ...