Recent years have seen the rise of extremist views in the opinion ecosystem we call social media. Allowing online extremism to persist has dire societal consequences, and efforts to mitigate it are continuously explored. Positive interventions, controlled signals that add attention to the opinion ecosystem with the aim of boosting certain opinions, are one such pathway for mitigation. This work proposes a platform to test the effectiveness of positive interventions, through the Opinion Market Model (Omm), a two-tier model of the online opinion ecosystem jointly accounting for both inter-opinion interactions and the role of positive interventions. The first tier models the size of the opinion attention market using the multivariate discrete-time Hawkes process; the second tier leverages the market share attraction model to model opinions cooperating and competing for market share given limited attention. On a synthetic dataset, we show the convergence of our proposed estimation scheme. On a dataset of Facebook and Twitter discussions containing moderate and far-right opinions about bushfires and climate change, we show superior predictive performance over the state-of-the-art and the ability to uncover latent opinion interactions. Lastly, we use Omm to demonstrate the effectiveness of mainstream media coverage as a positive intervention in suppressing far-right opinions.