A partial cooperative model that was recently proposed offers a balance between the two extreme scenarios commonly assumed in multi-agent systems, either completely competitive or fully cooperative agents. Partial cooperative agents act cooperatively in a distributed search process, as long as the outcome satisfies some threshold on their personal utility, otherwise, they act selfishly. While personal thresholds formalize intentions for cooperation in the existing model, inter agent relationships are not considered, although in realistic scenarios agents are often willing to act more cooperatively in their interactions with specific agents than with others, i.e., they have subjective cooperation intentions. We propose an extension to the partial cooperative model by introducing subjective intentions for cooperation. When making decisions on whether to perform cooperative actions agents take into consideration the identity of the agents these actions affect. A preliminary experimental evaluation demonstrates the advantage algorithms that consider the model have over algorithms that do not.