Many structured argumentation approaches proceed by constructing a Dung-style argumentation framework (AF) corresponding to a given knowledge base. While a main strength of AFs is their simplicity, instantiating a knowledge base oftentimes requires exponentially many arguments or additional functions in order to establish the connection. In this paper we make use of more expressive argumentation formalisms. We provide several novel translations by utilizing claim-augmented AFs (CAFs) and AFs with collective attacks (SETAFs). We use these frameworks to translate assumption-based argumentation (ABA) frameworks as well as logic programs (LPs) into the realm of graph-based argumentation.