  We prove existence of martingale solutions to a class of stochastic thin-film
equations for mobility exponents $n \in (2,3)$ and compactly supported initial
data. With the perspective to study free-boundary problems related to
stochastic thin-film equations in future work, we start from the
surface-tension driven stochastic thin-film equation with Stratonovich noise
and exploit the regime of coefficients in front of the Stratonovich correction
term (which is of porous-media-type) for which energy dissipation can be
established. By Bernis inequalities, third order spatial derivatives of
appropriate powers of the solution are controlled. Analytically, we rely on
approximation with $\mathbb{P}$-almost surely strictly positive solutions and
compactness methods based on energy-entropy estimates as well as martingale
identification techniques.
