  In this article, we present a new method to study uniqueness of form
extensions in a rather general setting. The method is based on the theory of
ordered Hilbert spaces and the concept of domination of semigroups. Our main
abstract result transfers uniqueness of form extension of a dominating form to
that of a dominated form. This result can be applied to a multitude of examples
including various magnetic Schr\"odinger forms on graphs and on manifolds.
