Can a steel pergola stand on a deck?

Yes, as long as the post bases sit on concrete rather than on the boards alone. On a timber deck the simplest route is pad footings between the joists with the base plates brought up to deck level. On a concrete slab the bases anchor straight into the slab, with anchors chosen for its thickness. Send us a photo of the patio and a note of how it is built up, and we will agree the fixing before production.