For over fifty years, evolutionary algorithms have been pivotal in solving diverse optimization problems across numerous domains. Among these, Genetic Algorithms (GAs) stand out for their adaptability and performance. The core operators of GAs are selection, crossover, and mutation, with crossover primarily responsible for gene inheritance. Traditionally, crossover is applied only once per parent pair, which may not adequately ensure the inheritance of good genes and can lead to undesirable gene propagation. Hence, applying the crossover many times starting from a single pair of parents could allow the search process to go deeper in the exploitation phase; thereby, increasing the probability of finding good genes. This paper challenges this limitation by proposing five novel deep crossover schemes for GAs: (1) In-Breadth, (2) In-Depth, and (3) Mixed-Breadth–Depth (MBD) with three variants. These schemes apply multiple crossover operations per parent pair, enabling a deeper search for high-quality genes, enhancing both exploration and exploitation capabilities. We integrate these schemes into the canonical GA and investigate their performance through two set of comparisons against the baseline GA and two state-of-the-art algorithms on multiple Traveling Salesman Problem (TSP) instances of varying sizes. Comparative analyses reveal that all the proposed GAs based deep crossover schemes outperform the canonical GA, while the GA-MBD (Fittest Historical Levels, Fittest All) succeeds to obtain the best performance when compared against the other peer approaches based on the Gap metric. Such results could encourage researchers to open the door towards a new field of computational intelligence coined as “Deep Evolutionary Computation”.