Language models (LMs) operate in evolving environments where adapting to new domains and linguistic shifts is critical. Continual pre-training (CPT) addresses this but introduces a strict stability-plasticity dilemma. While current approaches manage this via data replay or architectural changes, they largely treat the optimizer as a static component. We propose the Plasticity-Inducing Control Optimizer (PICO) to tackle this dilemma directly at the update level. The optimizer defines a utility-gated update together with a stochastic perturbation path controlled by periodic spectral sensitivity checks. Structural flags suppress the perturbation path while leaving the protected-gradient update active. Across the evaluated legal and medical streams, PICO exhibits a favorable stability–plasticity trade-off through optimizer-level control, while incurring a measurable spectral-monitoring cost. Code is available at https://github.com/infonet-gist/infonet-ai-pico.