Online extremism has severe societal consequences, including normalizing hate speech, user radicalization, and increased social divisions. Various mitigation strategies have been explored to address these consequences. One such strategy uses positive interventions: controlled signals that add attention to the opinion ecosystem to boost certain opinions. To evaluate the effectiveness of positive interventions, we introduce the Opinion Market Model (OMM), a two-tier online opinion ecosystem model that considers both inter-opinion interactions and the role of positive interventions. The size of the opinion attention market is modeled in the first tier using the multivariate discrete-time Hawkes process; in the second tier, opinions cooperate and compete for market share, given limited attention using the market share attraction model. We demonstrate the convergence of our proposed estimation scheme on a synthetic dataset. Next, we test OMM on two learning tasks, applying to two real-world datasets to predict attention market shares and uncover latent relationships between online items. The first dataset comprises Facebook and Twitter discussions containing moderate and far-right opinions about bushfires and climate change. The second dataset captures popular VEVO artists' YouTube and Twitter attention volumes. OMM outperforms the state-of-the-art predictive models on both datasets and captures latent cooperation-competition relations. We uncover (1) self- and cross-reinforcement between far-right and moderate opinions on the bushfires and (2) pairwise artist relations that correlate with real-world interactions such as collaborations and long-lasting feuds. Lastly, we use OMM as a testbed for positive interventions and show how media coverage modulates the spread of far-right opinions.