In this paper we examine an extension of the core concept for the 0/1 Multidimensional Knapsack Problem (MKP) towards general 0/1 Integer Programming (IP) by allowing negative profits, weights and capacities. The core concept provides opportunities for heuristically solving the MKP, achieving higher quality solutions and shorter run-times than general IP methods. We provide the theoretical foundations of the extended core concept and further provide computational experiments showing that we can achieve similar computational behavior for extended MKP instances with negative weights, profits and capacities.