Q: The episcopal conference where I work is considering raising the status of one of our patronal feasts to a solemnity. If the bishops decide to do it, what is the process for that request?
A: The Table of Liturgical Days lists as a solemnity the principal patron of a city or state (4a) and as a feast the principal patron of a country (8c).
According to the norms De Patronis Constituendis (Notitiae 9  263-266), n. 12 says that for good pastoral reasons, such as when the Patron has great importance in the history of the same region or is greatly honored by the faithful, the feast may become a solemnity.
Your episcopal conference would have to take a canonical vote on this. The bishop who serves as president of the conference then has to write to the Vatican’s Congregation for Divine Worship and the Discipline of the Sacraments reporting the results of the vote and explaining why the change is being requested (cf. Inter Oecumenici 27-29). If the CDWDS agrees, your conference will receive a decree raising the feast to a solemnity in your country.