This paper is devoted to applying the inverse Data Envelopment Analysis (InvDEA) in the simultaneous presence of desirable and undesirable factors. One of the most common ways to improve units' performance in the business environment is through activity synergies called units' merging. The present study models how to identify the inherited input/output from the units participating in the merger process to achieve the desired efficiency goal. The proposed models are established based on the InvDEA approach and multiple-objective programming tools. Sufficient conditions to estimate desirable and undesirable data are obtained using Pareto solutions to multi-objective programming problems. The theory extended in the study is explained by an application in the banking sector.