The interaction between multiple filamentary plasma eruptions is investigated by modelling the non-linear ideal MHD ballooning mode envelope equation with a mixed Eulerian and Lagrangian characterisation of the boundary conditions. The study of multiple plasma filaments is performed in a specific slab equilibrium susceptible to Rayleigh-Taylor instabilities. If the unstable system is initiated with three equal sized filaments, they erupt at the same rate, independently of each other, even in the non-linear regime. However, if one is initiated very slightly larger than the other two it causes a down-draft as it erupts upwards, which suppresses the smaller filaments. This suggests that those filaments which first enter the non-linear regime will dominate the plasma eruption dynamics.