I'll post a quote here on the different sorts of being that he attributes to his opponents, and his own opinion later.
"Esse reale est illud quod convenit rei ut existit formaliter et in natura propria et tale esse non convenit nisi singulari vel ei quod habet esse in singulari, quia solum singulare existit in natura propria per se et primo; universalia autem non existunt nisi ut habent esse in singularibus de quo esse intelligitur illud Philosophi in Praedicamentis, 'destructis primis impossible est aliquod aliorum remanere.
Esse vero intentionale est illud quod convenit rei ut habet esse repraesentative sive esse repraesentatum in aliquo alio ente reali, et quia repraesentari in aliquo alio obiective indifferenter convenit tam universali quam singulari, ideo esse intentionale convenit tam universali quam singulari, ideo esse intelligibile non magis appropriat sibi esse universale quam singulare nec e converso, et tale esse intentionale est debilius esse reali et ideo semper fundatur in ipso licet obiective.
Esse vero rationis convenit rei ut habet esse conceptus in sola consideratione intellectus operantis et tale cum sit esse diminutum, semper praesupponit alterum duorum praecedentium.
Dicunt igitur quod esse intentionale non est esse reale, quia potest convenire rei non existenti in natura propria, nec etiam esset esse rationis quia enti rationis repugnat existere in re; ei autem quod habet esse repraesentatum in aliquo et esse obiectivum in anima non repugnat existere in re, ideo istud esse intentionale est medium, ut dicunt, inter esse reale et esse rationis. Consimiliter distinguunt de distinctione, quia sicut triplex est esse, ita triplex est distinctio consequens, scilicet realis, intentionalis et rationis."
"Real being is that which befalls a thing as it exists formally and in its proper nature, and such being does not befall anything except a singular or that which has being in the singular, because only the singular exists in its proper nature per se and primarily. Universals, however, do not exist unless they have being in singulars, about which we should understand that statement of Aristotle that 'with the first things destroyed it is impossible for something of the others to remain.
Intentional being is that which befalls a thing as it has being representatively or to be represented in some other real being, and because to be represented in some other objectively is suited to both the universal and the singular indifferently, therefore intelligible being does not draw closer to universal being or singular being, and such intentional being is weaker than real being and therefore is always founded in it, although objectively.
Being of reason befalls a thing as it is a concept only in the consideration of an operating intellect and such being, since it is diminished, always presupposed one of the two preceding.
They say therefore, that intentional being is not real being, because it can befall a thing not existing in its proper nature, nor also is it a being of reason because it is repugnant to beings of reason to exist in reality; to that however which has representative being in something and objective being in the soul it is not repugnant to exist in reality, therefore that intentional being is medium, they say, between real being and being of reason. Likewise they distinguish about distinction, because just as there is a threefold being, so there is a threefold distinction consequent to it, namely, real, intentional, and rational.