Bellarmine and Molina ascribe cooperation not to nature but to new supernatural strength
What has been said makes it just as clear that the doctors of the Roman Church, Bellarmine and Molina himself among them, credit free choice's cooperation with grace not to the powers of nature but to the new powers our will has received through the help of grace.
They do not mean that free choice, when it consents to grace and follows its lead, does so by powers it already had, whose use was merely blocked until grace set it loose; Bellarmine complains that this is falsely charged against his side. They mean it does so by powers God has added to it beyond nature, so that the consent man's will gives to grace as it calls and rouses is a supernatural work, not a natural one.
Latin
LIV. Nec minus clarum est ex dictis Ecclesiae Romanae Doctores, ut Bellarminum, & Molinam ipsum, quod liberum arbitrium gratiae cooperatur, non tribuere naturae viribus, sed novis illis quas voluntas nostra per auxilium gratiae accepit. Nec eorum mentem esse, liberum arbitrium quum gratiae consentit, & ductum illius sequitur, id facere per vires quas jam ante habebat, & quarum solummodo usus impediebatur, antequam esset per gratiam solutum, quod suis falso imponi queritur Bellarminus, sed per vires quas Deus ipsi supra naturam addidit: ita ut consensus quem voluntas hominis gratiae vocanti & excitanti praebet, sit opus non naturale, sed supernaturale.