A stroller wagon is wider than a standard stroller even folded, so give it dedicated floor space and a strap rather than trying to stand it upright.
Pro tip: Fold the canopy down flat against the frame before collapsing the sides, most wagons fold more compactly in that order.
Watch out: A wagon stroller that unfolds partially during transit takes up significantly more space and can snag other cargo, confirm the fold lock is fully engaged.