  The stochastic thin-film equation with mobility exponent $n\in
[\frac{8}{3},3)$ on the one-dimensional torus with multiplicative Stratonovich
noise is considered. We show that martingale solutions exist for non-negative
initial values. This advances on existing results in three aspects: (1)
Non-quadratic mobility with not necessarily strictly positive initial data, (2)
Measure-valued initial data, (3) Less spatial regularity of the noise. This is
achieved by carrying out a compactness argument based solely on the control of
the $\alpha$-entropy dissipation and the conservation of mass.
