Adiabatic quantum-flux-parametron (AQFP) circuits are very low-power due to zero static power consumption and adiabatic switching operations. However, compared to other superconducting circuits, such as rapid single-flux-quantum logic, the operation frequency is relatively low and the latency is relatively large. In this work, we propose multi-excitation AQFP (ME-AQFP) circuits for high-speed and low-latency operations. In ME-AQFP, the intrinsic periodicity of the potential energy of a Josephson device with respect to applied magnetic fluxes is utilized to multiply operation frequencies and reduce latency. In a numerical simulation, we demonstrated an ME-AQFP AND gate, which operates at 10 GHz or 20 GHz with 5-GHz excitation currents. We also evaluated the energy efficiency of ME-AQFP circuits. In an experiment, we successfully demonstrated an ME-AQFP XOR gate and an ME-AQFP full adder.