A short run of proton-oxygen and oxygen-oxygen collisions is planned to take place at the Large Hadron Collider during LHC Run 3. The primary goal of this run is to improve the modeling of Cosmic-Ray interactions and to reduce the uncertainties associated with proton-Air cross-sections. While the inelastic cross-section will be measured directly, an array of very forward proton and neutron detectors introduced by the ATLAS and CMS experiments can allow going beyond the current physics research proposal, providing a unique opportunity to study elastic and diffractive interactions in pO collisions at the center of mass energies above TeV. This article presents the possible impact of proton and neutron tagging on the measurement of the elastic and diffractive components, as well as discusses the prospects of measuring the decay products of oxygen ions.