In the first place, generic unity refers to unity among multiple subjects according to the genus under which they may be subsumed. This definition of generic unity is set up in such a way that it cannot be compatible with numeric unity. The former concept presupposes multiple subjects for there to be unity among them, whereas the latter concept seems to consider the unity of a subject in itself, which is why there can only be one subject. It would not surprise me if [absolute] divine simplicity stems from numeric unity for this reason.
Humans are generically united in that, for example, each human possesses his own distinct rational faculty and moral character. Now, it is true that there is unity among the Father, Son, and Spirit unlike that of humans insofar as the wills of the former are mutually entailing rather than those of the latter, which can, at least at times, be mutually exclusive. Nevertheless, the divine persons are generically united in just the same sense humans are. Each divine person has a will, is good, omniscient, etc.
To focus on divine omniscience, here is an argument I made a few posts ago:
To be a person is to possess a mind capable of reflexively indexing a certain set of propositions. So, for example, the reasons that the Father, Son and Spirit are distinct persons or minds is that only the Father can think “I am unoriginate,” only the Son can think “I am eternally begotten,” and only the Spirit can think “I eternally proceed.”Without delving deeply into Christology, then, it should be noted that while two minds can pertain to one person, three persons cannot collectively possess one mind. The reason is obvious: distinct persons reflexively index certain propositions which other persons can't. If the Father, Son, and Spirit are distinct persons, there are at least two propositions which any given person cannot reflexively index. The Son and Spirit assent to the proposition "The Father is unoriginate," but neither can reflexively index it. Neither can say "I am unoriginate." Of course, none of the persons can reflexively index the proposition "Ryan Hedrich is writing a blog post," "Eve was the first woman," etc. either, but this is fairly trivial. It simply shows that:
...variances in reflexive thought do not imply that omniscience is impossible. The subject of the proposition "I am unoriginate" is, for the Father, "the Father," and both the Son and Spirit also assent to the proposition "the Father is unoriginate." Propositions are the meanings of declarative statements, and the meaning of the Father's thought "I am unoriginate" is synonymous with "the Father is unoriginate." Reflexive knowledge can accordingly be considered an indexation of propositional thought.What is the point of all of this? Well, Trinitarians do, in fact, affirm omniscience as a divine attribute. Trinitarians do, in fact, affirm the Father, Son, and Spirit to be distinct persons. Trinitarians do, in fact, affirm that only the Father can think "I am the Father," only the Son can think "I am the Son," and only the Spirit can think "I am the Spirit."
But the implication is that Trinitarians should therefore affirm that each person possesses His own, distinct omniscient mind. If there is any clear case against numeric unity from consideration of the divine attributes, this is it. Contrary to numeric unity, there is not only one subject of whom omniscience can be distinctly predicated. There are three subjects: the distinct persons of the Father, Son, and Spirit. Collapsing the subjects leads to Sabellianism. Collapsing the minds leads to the impossibility of any of the allegedly distinct persons to reflexively index a certain set of propositions which the other persons can't. This too would lead to Sabellianism. When we speak of the Trinity, we must think of three distinct divine persons and, respectively, three distinct omniscient minds.
Since there are a multitude of subjects-persons to whom the divine attribute of omniscience can distinctly apply, then in the context of Trinitarianism, numeric unity must be false and generic unity must be true.