We introduce the multiple access relay channel with generalized feedback (MARC-GF), which is more general than the known MARC (without feedback) and MAC-GF (without relay). In the MARC-GF, two sources, assisted by a common relay, send independent messages to a destination. The sources and relay each receives some feedback that may facilitate this communication. We propose and analyze a decode-and-forward scheme for the MARC-GF to obtain an achievable rate region. This scheme facilitates cooperation between the two sources, in addition to cooperation by the relay, via block Markov superposition encoding.