We propose a covariant technique to excavate physical bosonic string states by entire trajectories rather than individually. The approach is based on Howe duality: the string’s spacetime
Lorentz algebra commutes with a certain inductive limit of sp(•), with the Virasoro constraints
forming a subalgebra of the Howe dual algebra sp(•). There are then infinitely many simple trajectories of states, which are lowest–weight representations of sp(•) and hence of the Virasoro
algebra. Deeper trajectories are recurrences of the simple ones and can be probed by suitable
trajectory–shifting operators built out of the Howe dual algebra generators. We illustrate the formalism with a number of subleading trajectories and compute a sample of tree–level amplitudes.