Currently, the coupling of the European Electricity Markets has been fully achieved for the Day-Ahead Market. In the same time, a joint integrated Intra-Day Market based on the Continuous Trading mechanism is under implementation and it involves countries from West of Europe. However, some countries (e.g. Italy and Iberian countries) use the Discrete Auction mechanism and their integration implies the harmonization of the two trading mechanisms. A Hybrid Mechanism that represents the coordination of Continuous Trading and Discrete Auction has been discussed with two concrete proposals being made by Italy and Iberian countries. Thus, the aim of this paper is to propose an advanced algorithm which can simulate the clearing of the integrated European Intra-Day Market with any levels of coordination between Discrete Auction and Continuous Trading. The proposed model is formulated as a Mixed Integer Linear Problem and incorporates all market rules of both mechanisms. The algorithm is flexible enough to adapt to future changes. In addition, a case study that considers the current and near future market participants and covers an entire day of an Intra-Day Market is run by an iterative process to investigate the impact of the hybrid Intra-Day Market model on the Iberian countries and Italy according to their proposals. Moreover, the test cases represent realistic data in terms of number of variables and constraints, and in terms of complexity of the bids. The results of the paper show that, on one hand, the proposed market clearing model can be applied for different levels of Continuous Trading and Discrete Auction coordination and, on the other hand, the integration into the single European Intra-Day Market of Italy and Iberian countries can be beneficial for them. Therefore, the general conclusion is that the proposed market clearing model can be successfully used by the Power Exchanges currently integrated to solve the market or by the Power Exchanges not yet integrated to evaluate the impact of their future integration. On the other hand, the model can easily cope with any further changes in the market rules and represents a tool for future research, e.g. analysis of market participants behavior in future scenarios or evaluation of various financial instruments to manage the congestion of intra-border interconnectors.