Remora fish exhibit a remarkable ability to hitch-hike on large marine animals for long-distance transportation, serving as a significant source of inspiration for the development and control of underwater multiple robots. This paper is dedicated to exploring the hitch-hiking motions of multiple bionic robotic remoras. To begin, we construct an innovative robotic remora by taking inspiration from the biological structures of real remoras. Particularly, an adhesion system is designed to ensure secure and long-lasting attachments during underwater motion. Additionally, a flexible motion system, incorporating a pair of pectoral fins, a multi-link cascaded fish body, and a passive caudal fin, is developed to significantly enhance the required multimodal locomotion capabilities for hitch-hiking motions. Subsequently, to meet the collaborative hitch-hiking requirements, we propose a hitch-hiking motion control method based on a finite-state machine for multiple robotic remoras. Five sequential states are defined for the robotic remoras to execute during the collaborative adsorption process. Notably, an interaction and adjustment state is specifically designed to achieve the hitch-hiking sequence for multiple robotic remoras. Finally, extensive experiments are conducted, effectively demonstrating the superior multimodal locomotion capabilities of the newly developed robotic remora and the effectiveness of the proposed hitch-hiking control method for multiple robotic remoras. These finding can provide valuable insight for the cooperative control of underwater multiple robotic systems.