Can meditation strengthen the sense of self?

When I practice mindfulness meditation I can sometimes become acutely aware of my sense of self. It seems to go from a dull background awareness of self to a feeling that the sense of self is very pervasive and almost invasive into all aspects of experience. Naively I would expect that meditation would have the opposite affect and weaken the sense of self. In fairness sometimes it does but sometimes it appears to have this opposite effect. Is that a documented result of meditation. Is there advice out there from established teachers (of any schools) about working with this? Is it just me? Has anyone got advice based on their own experience?