The startings and endings of available process streams are usually time-dependent for a semiconsecutive (intermittent) process. The objective of this paper is to propose an optimization-based strategy for synthesizing a continuously operated mass-exchanger network (MEN) and its associated storage policy for treating process streams enriched with some undesirable components produced from an intermittently operated process. A periodically partitioned stagewise superstructure is presented for modeling the continuous MEN configuration, as well as the time-dependent operations for collecting process streams into storage tanks and releasing accumulated material into the continuous MEN for subsequent treatment. Not using any heuristics that are based on the concepts of pinch limitation, the proposed superstructure-based representation for the synthesis of continuous MENs for serniconsecutive processes is formulated as a mixed-integer nonlinear program (MINLP) for targeting the total annual cost (TAC). The coke oven gases (COG) problem from the literature is adapted and modified as an illustrative case to demonstrate the applicability of the proposed MEN synthesis method for serniconsecutive processes.