  We establish a multiparameter extension of the stochastic sewing lemma. This
allows us to derive novel regularity estimates on the local time of locally
non-deterministic Gaussian fields. These estimates are sufficiently strong to
derive regularization by noise results for SDEs in the plain. In this context,
we make the interesting and rather surprising observation that regularization
effects profiting from each parameter of the underlying stochastic field in an
additive fashion usually appear to be due to boundary terms of the driving
stochastic field.
