While user-side carbon reduction potential and quantity-price bidding enhance market flexibility, the uncertainty in cleared quantities may trigger demand-supply mismatch. To address diverse user needs, participants are categorized into three types based on their unmet demand for uncleared quantities and demand adjustment willingness, establishing a multi-stage clearing model for electricity-carbon coupled day-ahead markets. In the first stage, the clearing model with the goal of maximizing social welfare is established, and all users carry out settlement at that stage. In the second stage, the clearing model with the goal of minimizing total system cost is established,and users with demand for unsuccessful bids carry out deviation settlement. In the third stage, the clearing model with consideration of the users’carbon intensity is established, and users agreeing to demand adjustment carry out deviation settlement. The computational results of the improved PJM5 node system show that the model not only flexibly meets user demands, but also reduces system costs, carbon emissions, and user costs.