  In this note, we provide a generalization for the definition of a trisection
of a 4-manifold with boundary. We demonstrate the utility of this more general
definition by finding a trisection diagram for the Cacime Surface, and also by
finding a trisection-theoretic way to perform logarithmic surgery. In addition,
we describe how to perform 1-surgery on closed trisections. The insight gained
from this description leads us to the classification of an infinite family of
genus three trisections. We include an appendix where we extend two classic
results for relative trisections for the case when the trisection surface is
closed.
