Non-native species often acquire novel interspecific interactions, which are central to several hypotheses of invasion success, including biotic resistance and invasional meltdown. However, the outcome of these interactions is not often linked with the demographic evidence based on the full life cycle of the species. The Philippine Ground Orchid (Spathoglottis plicata) has invaded Puerto Rico and has acquired both negative and positive interspecific interactions involving the native weevil Stethobaris polita and the invasive red fire ant Solenopsis invicta, respectively. We studied a population in the Rio Abajo Forest, and asked how these interactions affect population demography by using a combination of field, experimental and modelling approaches. Stage-structured matrix population models based on four years of field observations showed that the population of S. plicata is growing at a rate ($łambda$) of 1.05 under natural conditions. When we modified fecundity values based on experimental exclusion of weevils and ants, the control treatment showed a similar $łambda$. Excluding weevils increased $łambda$ to 1.20, whereas the exclusion of ants decreased $łambda$ to 1.03. When we incorporate demographic and environmental stochasticity in our models, exclusion of invasive red fire ants significantly reduces the orchid abundance over time. Although weevils offer some biotic resistance to S. plicata, these effects do not prevent orchid population growth and expansion. On the other hand, invasive red fire ants have a positive effect on the invasive orchid's $łambda$, partially supporting the invasional meltdown hypothesis. This study presents a method that allows one to combine opposing mechanisms of species interactions within the same quantitative framework, and the results highlight the importance of considering acquired plant–animal interactions and stochastic processes when evaluating the population growth rates and dynamics of invasive plants.