  We present a detailed analysis of the International Pulsar Timing Array
(IPTA) Second Mock Data Challenge. We tested our analysis methods using the
open datasets, and then analyzed the closed datasets. In both the open and the
closed datasets, we were able to detect some, but not all, of the injected
gravitational wave signals. This work presents two search cases that are not
well explored in the pulsar timing array (PTA) literature: a simultaneous
search for a stochastic GW background and an individual loud super-massive
black hole binary (SMBHB) and a simultaneous search for two SMBHB sources.
While we have constructed a cohesive framework for performing these GW
searches, our analyses required fine-tuning of the sampling method used in
order to appropriately converge. Given the nature of real PTA data in which
multiple sources will be present in data, improved techniques will be required
in the future to accurately detect and characterize these GW signals.
