We develop and analyze a new approach for simultaneously computing multiple solutions to the Helmholtz equation for different frequencies and different forcing functions. The new Multi-Frequency WaveHoltz (MFWH) algorithm is an extension of the original WaveHoltz method and both are based on time-filtering solutions to an associated wave-equation. With MFWH, the different Helmholtz solutions are computed simultaneously by solving a single wave equation combined with multiple time filters. The MFWH algorithm defines a fixed-point iteration which can be accelerated with Krylov methods such as GMRES. The solution of the wave equation can be efficiently solved with implicit time-stepping using as few as five time-steps per period. Discretization errors in time can be completely removed by various adjustments. Numerical results are given to confirm the convergence theory when solving energy conserving problems.