If the title of this topic makes you uneasy at all, you have something to learn.
According to the SSPX website, we can pray for the pope's “objective intentions” as opposed to “personal, subjective intentions”
The six objective intentions of the Holy Father, traditionally understood, are: the exaltation of the Church, the propagation of the Faith, the extirpation of heresy, the conversion of sinners, concord between Christian princes, and the further welfare of the Christian people.