We are sorry to have to tell you that until this very moment there is no way to increase the Tuning Limit on your favorite Guardians of Souls. It might become possible sometime later, but at least for now it is not.
Keep in mind that the stronger the Guardian of the Spirit, the lower the Tuning Limit. Spirit Guardians who focus on attack and upgrade damage have a lower Tuning Limit than passive Spirit Guardians as a balancing technique.
We are sorry we could not tell you exactly How to Increase Attunement Limit in Nioh 2, so we will be on the lookout very closely in case the developers allow us to increase this limit at any time, bring you everything about it so you know how to do it.