This work proposes a novel multi-robot task allocation framework for robots that can switch between multiple modes, e.g., flying, driving, or walking. We first provide a method to encode the multi-mode property of robots as a graph, where the mode of each robot is represented by a node. Next, we formulate a constrained optimization problem to decide both the task to be allocated to each robot as well as the mode in which the latter should execute the task. The robot modes are optimized based on the state of the robot and the environment, as well as the energy required to execute the allocated task. Moreover, the proposed framework is able to encompass kinematic and dynamic models of robots alike. Furthermore, we provide sufficient conditions for the convergence of task execution and allocation for both robot models.