The study of hadronic showers, which are produced by cosmic rays penetrating the Earth's atmosphere, is essential for shedding light on the origins and characteristics of high-energy particles originating from space and reaching our planet. At the Large Hadron Collider at CERN, there are plans to conduct a short run of proton--oxygen collisions in 2025 to refine the modeling of hadronic showers. This work explores the potential impact on constraining models of hadronic showers by measuring interactions facilitated by color-neutral objects such as photons, pomerons, and pions. These interactions are often characterized by high-energy protons or neutrons produced at forward rapidities and can be tagged using dedicated forward proton and neutron detectors.