In our paper [13], we have proposed a logical encoding of argumentation frameworks with higher-order interactions (i.e. attacks or supports whose targets are arguments or other attacks or supports) with an evidential meaning for supports, such frameworks are called REBAF. With this encoding, we are able to characterize the semantics of REBAF under the form of specific logical models. Nevertheless this encoding has two important drawbacks: first the handling of support cycles has some weaknesses and secondly the collective interactions (i.e. attacks or supports whose source is a set of arguments and not only one argument) are not taken into account. The current paper proposes an improvement of this encoding for solving these drawbacks.