The prepositions παρά and ὑπό with the dative signal an agent, at least in some authors.
Homer uses ὑπό with the dative in the same contexts as the dative of the agent, i.e. with a limited group of verbs, of which δάμνημι ‘to overpower’ is the most important.
Demosthenes uses παρά with the dative in the same way as ὑπό (or παρά) with the genitive. In an attempt to imitate Homer, later epic writers (such as Apollonius of Rhodes, Quintus or Nonnus) avoid the genitive with ὑπό and prefer the dative.
ὁ μὲν γὰρ ὅσῳ πλείον’ ὑπὲρ τὴν ἀξίαν πεποίηκε τὴν αὑτοῦ, τοσούτῳ θαυμαστότερος παρὰ πᾶσι νομίζεται
For the more he raised himself above his own worth, the more he was admired by everybody.