  In 2012, N. Williams and the second author showed that on order ideals of
ranked partially ordered sets (posets), rowmotion is conjugate to (and thus has
the same orbit structure as) a different toggle group action, which in special
cases is equivalent to promotion on linear extensions of posets constructed
from two chains. In 2015, O. Pechenik and the first and second authors extended
these results to show that increasing tableaux under K-promotion naturally
corresponds to order ideals in a product of three chains under a toggle group
action conjugate to rowmotion they called hyperplane promotion. In this paper,
we generalize these results to the setting of arbitrary increasing labelings of
any finite poset with given restrictions on the labels. We define a
generalization of K-promotion in this setting and show it corresponds to a
toggle group action we call toggle-promotion on order ideals of an associated
poset. When the restrictions on labels are particularly nice (for example,
specifying a global bound on all labels used), we show that toggle-promotion is
conjugate to rowmotion. Additionally, we show that any poset that can be nicely
embedded into a Cartesian product has a natural toggle-promotion action
conjuate to rowmotion.
