This paper presents a hierarchical nonlinear control algorithm for the real-time planning and control of cooperative locomotion of legged robots that collaboratively carry objects. An innovative network of reduced-order models subject to holonomic constraints, referred to as interconnected linear inverted pendulum (LIP) dynamics, is presented to study cooperative locomotion. The higher level of the proposed algorithm employs a supervisory controller, based on event-based model predictive control (MPC), to effectively compute the optimal reduced-order trajectories for the interconnected LIP dynamics. The lower level of the proposed algorithm employs distributed nonlinear controllers to reduce the gap between reduced- and full-order complex models of cooperative locomotion. In particular, the distributed controllers are developed based on quadratic programming (QP) and virtual constraints to impose the full-order dynamical models of each agent to asymptotically track the reduced-order trajectories while having feasible contact forces at the leg ends. The paper numerically investigates the effectiveness of the proposed control algorithm via full-order simulations of a team of collaborative quadrupedal robots, each with a total of 22 degrees of freedom. The paper finally investigates the robustness of the proposed control algorithm against uncertainties in the payload mass and changes in the ground height profile. Numerical studies show that the cooperative agents can transport unknown payloads whose masses are up to 57%, 97%, and 137% of a singles agent's mass with a team of two, three, and four legged robots.