  In this paper we generalize the theory of multiplicative $G$-Higgs bundles
over a curve to pairs $(G,\theta)$, where $G$ is a reductive algebraic group
and $\theta$ is an involution of $G$. This generalization involves the notion
of a multiplicative Higgs bundle taking values in a symmetric variety
associated to $\theta$, or in an equivariant embedding of it. We also study how
these objects appear as fixed points of involutions of the moduli space of
multiplicative $G$-Higgs bundles, induced by the involution $\theta$.
