  The large-scale analysis task of deciphering gravitational wave signals in
the LISA data stream will be difficult, requiring a large amount of
computational resources and extensive development of computational methods. Its
high dimensionality, multiple model types, and complicated noise profile
require a global fit to all parameters and input models simultaneously. In this
work, we detail our global fit algorithm, called "Erebor," designed to
accomplish this challenging task. It is capable of analysing current
state-of-the-art datasets and then growing into the future as more pieces of
the pipeline are completed and added. We describe our pipeline strategy, the
algorithmic setup, and the results from our analysis of the LDC2A Sangria
dataset, which contains Massive Black Hole Binaries, compact Galactic Binaries,
and a parameterized noise spectrum whose parameters are unknown to the user. We
recover posterior distributions for all 15 (6) of the injected MBHBs in the
LDC2A training (hidden) dataset. We catalog $\sim12000$ Galactic Binaries
($\sim8000$ as high confidence detections) for both the training and hidden
datasets. All of the sources and their posterior distributions are provided in
publicly available catalogs.
