Notable orders traditionally considered "near passerines" but not placed in the Passerae of the Sibley-Ahlquist taxonomy are Coliiformes, Coraciiformes, Piciformes and Trogoniformes (see below for why this is significant).
While the Sibley-Ahlquist taxonomy certainly represents a monumental endeavour and has some strong points (namely the recognition of the Galloanserae), basically everything about this "parvclass" is today regarded as utter fiction, brought about by the methodological and analytical problems of the phenetic DNA-DNA hybridization analysis. The "Passerae" are one of the most seriously flawed systematic proposals in modern ornithology, perhaps rivalled only by the suggestion (based as it was on early cladistic analyses) that Hesperornithes, Gaviiformes and Podicipediformes form a monophyletic group. In sheer scope of their falseness, however, the "Passerae" are in post-Linnean ornithology matched only by the ecomorphology-based "taxa" of Charles Lucien Jules Laurent Bonaparte's mid-19th century Conspectus Generum Avium.
At present, the closest living relatives of passerines are held to be the Piciformes, followed by the Coraciiformes. Neither of these two was included in the "Passerae". The Coliiformes and Trogoniformes, while of unclear relationships among the "higher landbirds", are also candidates for inclusion in a "near passerine" superorder. Insofar, it is actually hard to be less correct regarding the relationships of the perching birds than the Sibley-Ahlquist taxonomy.
Parvclasses are generally not used at all in modern ornithological systematics, as the understanding of neoavian relationship has not progressed to a point where use of such a taxonomic rank would seem sensible.