There is substantial experimental evidence that learning and memory-related behaviours rely on local synaptic changes, but the search for distinct plasticity rules has been driven by human intuition, with limited success for multiple, co-active plasticity rules in biological networks. More recently, automated meta-learning approaches have been used in simplified settings, such as rate networks and small feed-forward spiking networks. Here, we develop a simulation-based inference (SBI) method for sequentially filtering plasticity rules through an increasingly fine mesh of constraints that can be modified on-the-fly. This method, filter SBI, allows us to infer entire families of complex and co-active plasticity rules in spiking networks. We first consider flexibly parameterized doublet (Hebbian) rules, and find that the set of inferred rules contains solutions that extend and refine -and also reject- predictions from mean-field theory. Next, we expand the search space of plasticity rules by modelling them as multi-layer perceptrons that combine several plasticity-relevant factors, such as weight, voltage, triplets and co-dependency. Out of the millions of possible rules, we identify thousands of unique rule combinations that satisfy biological constraints like plausible activity and weight dynamics. The resulting rules can be used as a starting point for further investigations into specific network computations, and already suggest refinements and predictions for classical experimental approaches on plasticity. This flexible approach for principled exploration of complex plasticity rules in large recurrent spiking networks presents the most advanced search tool to date for enabling robust predictions and deep insights into the plasticity mechanisms underlying brain function.