Though any general predicate might correspond to a Form (according to Plato's view at one stage or another), and the question of self-predication might be approached in general, Plato more specifically needs to uphold his view that the Form of the Good is itself good, is "greater in dignity and might" than all other Forms. If he wants to say this, he has to then confront the consequences of such self-predication more broadly.
Down the line, one approach to resolving the issue arose in theology, in the notion of analogical predication. Allow (loosely or not) that God is the Form of the Good, but that God is essentially different from creatures. So the goodness of a creature comes from participating in the will of God (in the appropriate way), but the "goodness" of God is actually something like "supergoodness," an internally different predicate. From the SEP article on medieval theories of analogy (sec. 6):
Despite the vast modern literature devoted to Aquinas’s theory of analogy, he has very little to say about analogy as such. He uses a general division into equivocal, univocal, and analogical uses of terms, and he presents both of the threefold divisions of analogy mentioned in the previous section, but he offers no prolonged discussion, and he writes as if he is simply using the divisions, definitions, and examples with which everyone is familiar. His importance lies in the way he used this standard material to present an account of the divine names, or how it is we can meaningfully use such words as ‘good’ and ‘wise’ of God.
The background to this account has to be understood in terms of Aquinas’s theology and metaphysics. Three doctrines are particularly important. First, there is the distinction between being existent, good, wise, and so on, essentially, and being existent, good, wise, and so on, by participation. God is whatever he is essentially, and as a result he is existence itself, goodness itself, wisdom itself. Creatures are existent, good, wise, only by sharing in God’s existence, goodness, and wisdom, and this sharing has three features. It involves a separation between the creature and what the creature has; it involves a deficient similarity to God; and it is based on a causal relation. What is essentially existent or good is the cause of what has existence or goodness by participation. Second, there is the general doctrine of causality according to which every agent produces something like itself. Agent causality and similarity cannot be separated. Third, there is Aquinas’s belief that we are indeed entitled to claim that God is existent, good, wise, and so on, even though we cannot know his essence.
Against this background, Aquinas asks how we are to interpret the divine names. He argues that they cannot be purely equivocal, for we could not then make intelligible claims about God. Nor can they be purely univocal, for God’s manner of existence and his relationship to his properties are sufficiently different from ours that the words must be used in somewhat different senses. Hence, the words we use of God must be analogical, used in different but related senses. To be more precise, it seems that such words as ‘good’ and ‘wise’ must involve a relationship to one prior reality, and they must be predicated in a prior and a posterior sense, for these are the marks of analogical terms.
Nonetheless, the divine names do not function exactly like ordinary analogical terms such as ‘healthy’. We need to begin by making use of the distinction between the thing signified (a nature or property) and the mode of signifying. All the words we use have a creaturely mode of signifying in that they imply time and composition, neither of which can pertain to God. When speaking of God, we must recognize this fact, and attempt to discount it. To say “God is good” is not to imply that God has a separable property, goodness, and that he has it in a temporally limited way. God is eternally identical to goodness itself. But even when we have discounted the creaturely mode of signifying, we are left with the fact that God’s goodness is not like our goodness. This is where the analogy of attribution enters the picture.