  The present paper is devoted to the study of backward stochastic differential
equations with mean reflection formulated by Briand et al. [7]. We investigate
the solvability of a generalized mean reflected BSDE, whose driver also depends
on the distribution of the solution term $Y$. Using a fixed-point argument, BMO
martingale theory and the $\theta$-method, we establish the existence and
uniqueness result for such BSDEs in several typical situations, including the
case where the driver is quadratic with bounded or unbounded terminal
condition.
