In many real-world scenarios, an individual's local social network carries significant influence over the opinions they form and subsequently propagate. In this paper, we propose a novel diffusion model -- the Pressure Threshold model (PT) -- for dynamically simulating the spread of influence through a social network. This model extends the popular Linear Threshold (LT) model by adjusting a node's outgoing influence in proportion to the influence it receives from its activated neighbors. We examine the Influence Maximization (IM) problem under this framework, which involves selecting seed nodes that yield maximal graph coverage after a diffusion process, and describe how the problem manifests under the PT model. Experiments on real-world networks, supported by enhancements to the open-source network-diffusion library CyNetDiff, reveal that greedy IM under PT can yield seed sets distinct from those under LT. Furthermore, the analyses show that densely connected networks amplify pressure effects far more strongly than sparse networks.