Most simulations of neuroplasticity in memristors, which are potentially used to develop artificial synapses, are confined to the basic biological Hebbian rules. However, the simplex rules potentially can induce excessive excitation/inhibition, even collapse of neural activities, because they neglect the properties of long-term homeostasis involved in the frameworks of realistic neural networks. Here, we develop organic CuPc-based memristors of which excitatory and inhibitory conductivities can implement both Hebbian rules and homeostatic plasticity, complementary to Hebbian patterns and conductive to the long-term homeostasis. In another adaptive situation for homeostasis, in thicker samples, the overall excitement under periodic moderate stimuli tends to decrease and be recovered under intense inputs. Interestingly, the prototypes can be equipped with bio-inspired habituation and sensitization functions outperforming the conventional simplified algorithms. They mutually regulate each other to obtain the homeostasis. Therefore, we develop a novel versatile memristor with advanced synaptic homeostasis for comprehensive neural functions.