In this paper we study the multiple access channel (MAC) with combined cooperation and partial cribbing and characterize its capacity region. Cooperation means that the two encoders send a message to one another via a rate-limited link prior to transmission, while partial cribbing means that each of the two encoders obtains a deterministic function of the other encoder's output with or without delay. Prior work in this field dealt separately with cooperation and partial cribbing. However, by combining these two methods we can achieve significantly higher rates. Remarkably, the capacity region does not require an additional auxiliary random variable (RV) since the purpose of both cooperation and partial cribbing is to generate a common message between the encoders. In the proof we combine methods of block Markov coding, backward decoding, double rate-splitting, and joint typicality decoding. Furthermore, we present the Gaussian MAC with combined one-sided cooperation and quantized cribbing. For this model, we give an achievability scheme that shows how many cooperation or quantization bits are required in order to achieve a Gaussian MAC with full cooperation/cribbing capacity region. After establishing our main results, we show that in a state-dependent MAC with cooperation, where the state is known at a partially cribbing encoder and at the decoder, only one auxiliary RV is needed to incorporate both the cribbing and the cooperation. However, there are cases where more than one auxiliary RV is needed, e.g., when the cooperation and cribbing are not used for the same purposes. We present a MAC with an action-dependent state where the action is based on the cooperation but not on the cribbing. Therefore, in this case more than one auxiliary RV is needed. We deduce a general rule for this result.