  In this paper, we establish the well-posedness and optimal trajectory
regularity for the solution of stochastic evolution equations with generalized
Lipschitz-type coefficients driven by general multiplicative noises. To ensure
the well-posedness of the problem, the linear operator of the equations is only
need to be a generator of a $\CC_0$-semigroup and the proposed noises are quite
general, which include space-time white noise and rougher noises. When the
linear operator generates an analytic $\CC_0$-semigroup, we derive the optimal
trajectory regularity of the solution through a generalized criterion of
factorization method.
