Due　to　important　applications　in　viral　marketing,　influence　maximization　(IM)　has　become　a　well-studied　problem.　It　aims　at　finding　a　small　subset　of　initial　users　so　that　they　can　deliver　information　to　the　largest　amount　of　users　through　the　word-of-mouth　effect.　The　original　IM　only　considers　a　singleton　item.　And　the　majority　of　extensions　ignore　the　relationships　among　different　items　or　only　consider　their　competitive　interactions.　In　reality,　the　diffusion　probability　of　one　item　will　increase　when　users　adopted　supplementary　products　in　advance.　Motivated　by　this　scenario,　we　propose　a　supplementary　independent　cascade　(IC)　and　discuss　the　supplementary　IM　problem.　Our　problem　is　NP-hard,　and　the　computation　of　the　objective　function　is　#P-hard.　We　notice　that　the　diffusion　probability　will　change　when　considering　the　impact　of　its　supplementary　product.　Therefore,　the　efficient　reverse　influence　sampling　(RIS)　techniques　cannot　be　applied　to　our　problem　directly　even　though　the　objective　function　is　submodular.　To　address　this　issue,　we　utilize　the　sandwich　approximation　(SA)　strategy　to　obtain　a　data-dependent　approximate　solution.　Furthermore,　we　define　the　supplementary-based　reverse　reachable　(SRR)　sets　and　then　propose　a　heuristic　algorithm.　Finally,　the　experimental　results　on　three　real　datasets　support　the　efficiency　and　superiority　of　our　methods.