Shastri and Ajjanagadde have described a neurally plausible system for knowledge representation and reasoning that can represent systematic knowledge involving n-ary predicates and variables, and perform a broad class of reasoning with extreme efficiency. The system maintains and propagates variable bindings using temporally synchronous — i.e., in-phase — firing of appropriate nodes. This paper extends the reasoning system to incorporate multiple instantiation of predicates, so that any predicate can now be instantiated with up to k dynamic facts, k being a system constant. The ability to accommodate multiple instantiations of a predicate allows the system to handle a much broader class of rules; the system can even handle limited recursion (up to k levels). Though the time and space requirements increase by a constant factor, the extended system can still answer queries in time proportional to the length of the shortest derivation of the query and is independent of the size of the knowledge base.