  This paper is devoted to a global stochastic maximum principle for
conditional mean-field forward-backward stochastic differential equations
(FBSDEs, for short) with regime switching. The control domain is unnecessarily
convex and the driver of backward stochastic differential equations (BSDEs, for
short) could depend on $Z$. Different from the case of non-recursive utility,
the first-order and second-order adjoint equations are both high-dimensional
linear BSDEs. Based on the adjoint equations, we reveal the relations among the
terms of the first- and second-order Taylor's expansions. A general maximum
principle is proved, which develops the work of Nguyen, Yin, and Nguyen [22] to
recursive utility. As applications, the linear-quadratic problem is considered
and a problem with state constraint is studied.
