To develop hippocampal prosthetic devices that can restore the memory-dependent cognitive functions lost in diseases or injuries, it is essential to build a computational model that sufficiently captures the transformations of multiple memories performed by hippocampal sub-regions. A universal model with a single set of coefficients for all memories is desirable, since it can transform the memories without explicitly knowing what those memories represent and thus avoids switching between multiple models for multiple memories in implementation. In this study, we test the feasibility of such universal models of hippocampal CA3-CA1 by estimating the multi-input, multi-output (MEMO) nonlinear dynamic models using input (CA3) and output (CA1) spike trains recorded during multiple behavioral events representing multiple memories from rats performing a delayed nonmatch-to-sample task. We further statistically evaluated the model performances of the MEMO models on the different events. Results show that the models accurately replicate the output spike patterns during those events, and thus can be used as event-invariant nonlinear dynamic models that continuously predict the ongoing CA1 spatio-temporal patterns as the ongoing CA3 spatio-temporal patterns unfold.