The capacity of an order-d associative memory model is O(N^d/logN). The exponential growth of the capacity with respect to d gives higher order models (d > 1) significant advantage over the Hopfield network, whose capacity is limited to O(N/logN). One problem with the higher order models is that their data processing can not be implemented on network models that are widely considered biologically feasible. In this paper, we propose a new higher order associative memory model that can be implemented with a collection of a simple McCulloch-Pitts neuron model with one extension: the synapses or network weights being adaptive or plastic. The plasticity is achieved by allowing the synaptic weights to change along the projection of the current network state to a correlation tensor. We show that our model guarantees convergence with a weak constraint, retains the capacity and basin of attraction of the higher correlation model, and is more robust against noise than the higher correlation model. Extensive numerical experiments agree with our claim. We also propose a d = 2 model with an approximate correlation tensor that brings reduction of computational cost during the retrieval phase. Numerical experiments show that the cost can be reduced by half without affecting the retrieval performance significantly.