We introduce a new framework for generating counterfactual recourse in machine learning that embraces a "human-in-the-loop" approach by incorporating user preferences. Traditional counterfactual tools neglect individual user preferences when adjusting features. To address this, we tackle recourse generation as a multi-objective optimization problem, integrating conventional constraints with user preferences. Our framework, termed HIP-CORE, is specifically crafted to estimate these preferences during the counterfactual generation phase. We also introduce the "Personal Validity" as a measure of the effectiveness of recourse for individual users. Through extensive theoretical and empirical analysis, we validate the benefits of our proposal. Overall, this work enhances counterfactual reasoning and paves the way for more personalized algorithmic recourse. Code is available at https://github.com/federicosiciliano/hip-core.git.