  We recently introduced a T-duality covariant mechanism to compute all-order
higher-derivative interactions in the heterotic string. Here we extend the
formalism to account for a two-parameter family of corrections that also
include the bosonic string and HSZ theory. We use our result to compute the
full second order Double Field Theory (DFT) for generic values of the
parameters, including the generalized Green-Schwarz transformation and its
invariant action.
