What are the church's teachings on what is morally licit to increase fertility?
The general rule is that if something in the body is not working as it should, we may do what we can to get it fixed. Or if a part of the body is diseased, we may get it healed. We are restoring our bodies to how it was designed to function naturally.
For example, a woman may not ovulate regularly or often. A hormone that encourages her body to ovulate more often, as it should, is acceptable. Or a tube may be clogged that carries the ovum. It may be cleared. None of these techniques interferes with the unitive and procreative aspects of the marital act. That means that the husband and wife still join together in the marital act, open to children.