"We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond to the case) for arbitrary -Souslin quasi-orders on any Polish space, for an infinite cardinal smaller than the cardinality of R. These generalizations yield a variety of results concerning the complexity of the embeddability relation between graphs or lattices of size , the isometric embeddability relation between complete metric spaces of density character , and the linear isometric embeddability relation between (real or complex) Banach spaces of density "--