We study the effect of non-trivial sound speeds on local-type non-Gaussianity during multiple-field inflation. To this end, we consider a model of multiple-field DBI and use the deltaN formalism to track the super-horizon evolution of perturbations. By adopting a sum separable Hubble parameter we derive analytic expressions for the relevant quantities in the two-field case, valid beyond slow variation. We find that non-trivial sound speeds can, in principle, curve the trajectory in such a way that significant local-type non-Gaussianity is produced. Deviations from slow variation, such as rapidly varying sound speeds, enhance this effect. To illustrate our results we consider two-field inflation in the tip regions of two warped throats and find large local-type non-Gaussianity produced towards the end of the inflationary process.