We produce new non-Kähler, non-Einstein, complete expanding gradient Ricci
solitons with conical asymptotics and underlying manifold of the form $\R^2
\times M_2 \times \cdots \times M_r$, where $r \geq 2$ and $M_i$ are arbitrary
closed Einstein spaces with positive scalar curvature. We also find numerical
evidence for complete expanding solitons on the vector bundles whose sphere
bundles are the twistor or ${\rm Sp}(1)$ bundles over quaternionic projective
space.