This paper discusses the transit model fitting and multiple-planet search algorithms and performance of the Kepler Science Data Processing Pipeline, developed by the Kepler Science Operations Center (SOC). Threshold Crossing Events (TCEs), which are transit candidate events, are generated by the Transiting Planet Search (TPS) component of the pipeline and subsequently processed in the Data Validation (DV) component. The transit model is used in DV to fit TCEs in order to characterize planetary candidates and to derive parameters that are used in various diagnostic tests to classify them. After the signature associated with the TCE is removed from the light curve of the target star, the residual light curve goes through TPS again to search for additional TCEs. The iterative process of transit model fitting and multiple-planet search continues until no TCE is generated from the residual light curve or an upper limit is reached. The transit model fitting and multiple-planet search performance of the final release (9.3, January 2016) of the pipeline is demonstrated with the results of the processing of 4 years (17 quarters) of flight data from the primary Kepler Mission. The transit model fitting results are accessible from the NASA Exoplanet Archive. The final version of the SOC codebase is available through GitHub.
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