In chemoinformatics, Quantitative Structure Activity and Property Relationships (QSAR and QSPR) are two fields which aim to predict properties of molecules thanks to computational techniques. In these fields, graph kernels provide a powerful tool which allows to combine the natural encoding of molecules by graphs with usual statistical tools. However, some molecules May have a same graph but differ by the three dimensional orientation of their atoms in space. These molecules, called stereoisomers, May have different properties which cannot be correctly predicted using usual graph encodings. In a previous study we proposed to encode the stereoisomerism property of each atom by a local subgraph, called minimal stereo subgraph, and we designed a kernel based on the comparison of bags of such subgraphs. This kernel allows to predict properties induced by the stereoisomerism which cannot be correctly predicted using usual graph kernels. However, it has two major drawbacks : it considers each minimal stereo subgraph without taking into account its surroundings, and it considers that two non identical minimal stereo subgraphs have a null similarity. In this paper we present three extensions to tackle those drawbacks. The first extension allows to take into account interactions between minimal stereo subgraphs. The second extension allows to compare the neighborhood of minimal stereo subgraphs. And finally, the third extension provides a measure of similarity between different minimal stereo subgraphs.