You are able to acquire more Breaths in various methods. By meditating, you can gather Breaths from the world around you. With enough experience, you will learn to increase the amount of Breaths you receive per week, and will even be able to lower the time between cycles. Killing other beings will allow you to gather Breaths from them.
You are able to directly funnel Breaths into your Divine Breath at a near-perfect rate through dedicated mediation. This special form of meditation will not allow you to increase your stock of normal Breaths while in progress.
Slaying familiar types of entities increases the amount of Breaths you receive. Sometimes, upon recalling your Breaths from Awakened objects you consistently use, you will receive more than you put in.