Inclusive one- and multi-nucleon removal cross sections have been measured for several Sn, Sb and Te isotopes just beyond the N=82 neutron shell closure. The beams were produced in the projectile fission of a 238U beam at the Radioactive Isotope Beam Factory at RIKEN. The experimental cross sections are compared to predictions from the most recent version of the Liege intranuclear cascade model. Although the overall agreement is good, severe discrepancies are observed for the cases of one- and two-neutron removal from 134Sn and 135Sb projectiles and one-proton knockout from all measured N=84 isotones. These discrepancies, as well as the relevance of quasi-elastic reaction channels to the one-neutron removal cross sections, are discussed. In addition, the measured inclusive one-proton knockout cross section for the semi-magic 134Sn projectile is compared to eikonal direct reaction theory calculations to assess if the suppression factors to these calculated cross sections, deduced from data on reactions of lighter projectile nuclei, are also applicable to heavy nuclei.