A secret sharing scheme is said to be d-multiplicative if the scheme allows the players to multiply shared d secrets by locally converting their shares into an additive sharing of the product. In the previous work, the following negative result for perfect secret sharing has been shown: The d-multiplicative secret sharing for d players is impossible. This paper extends the impossibility result to non-perfect secret sharing. Our main result is a proof that d-multiplicative secret sharing for d players is impossible even if every player has partial information on the secret (e.g., all but one bit). This result means that there is no need to relax the privacy requirement with leakage of partial information only for the purpose of d-multiplication.