We propose a new inference method for multiple change-point detection of high-dimensional time series. The proposed approach targets at dense or spatially clustered cross-sectional signals. An l2-aggregated statistics via a novel Two-Way MOSUM is adopted in the cross-sectional dimension to detect multiple mean shifts for high-dimensional dependent data, and then followed by maximum over time. On the theory front, we develop the asymptotic theory concerning the limiting distributions of the change-point test statistics under both the null and alternatives, and we establish the consistency of the estimated break dates. The core of our theory is to extend a high-dimensional Gaussian approximation theorem to non-stationary dependent data, in particular for an l2 type statistics accounting for proportional jumps which is not available in the literature. Moreover, to facilitate the inference of breaks with natural clusters in the cross-sectional dimension, we also provide asymptotic properties of the test statistics with spatial dependence. Numerical simulations demonstrate the power enhancement of our newly proposed testing method relative to other existing techniques.