Agape is an interesting Greek term. Ask five people; you'll get seven different definitions. Most agree that it is a unique kind of Love. However, a survey of the New Testament and one soon discovers that Agape wasn’t the special word it would later become. Agape (and its conjugates) were used in various contexts and often interchangeable with another Greek kind of Love. While the word Eros (another Greek word for a kind of Love in the form of desire) is never used in the New Testament, there are examples where Agape is used in ways that communicate self-love /desire. All this to say that we can't build a scriptural case for Agape as a special kind of super Love.
However, words change and evolve, which is the case with Agape. It morphed in the sense that it connotes a special kind of all-inclusive, self-giving kind of Love, or divine Love if you will. The word Agape evolved and became a contrast to at least two other predominant first-century cultural views of Love.
Old Greek ethics focused on the highest good … that, in every respect, the highest good satisfies the individual. Eros (vulgar or Heavenly, Plato, 1 Symposium) was a central idea of Greek Love, typically individualistic, ego-centred, "personal happiness in the moment" focused desire.
Plato explores the idea of Eros/Love in his Symposium, and his protagonist, Socrates, argues that to desire beauty (or the good) means those desiring it lack that beauty (good). To extrapolate this, for God to desire something is to say God lacks something that can only be satisfied by something else. A God who lacks is not conducive to the idea of a perfect God.
Those who repurposed Agape would counter that God does not love from lack/desire; rather, God loves out of the fullness of God's love nature. It is also possible to desire, in the best sense, for the sake of the well-being of another without resulting in a deficit. Eros as desire can be a valid expression of genuine Love. Scriptures express many things that God desires. Consider the legitimate desire of God (if you like 'the will of God'), which legitimately flow from the abundance of God's love nature.
A Jewish perspective of Love was, in many ways, counter-cultural in that Love extended beyond the individual to the community of fellow Jews (and some novel ideas about the just treatment of strangers). This was a significant shift in perspective from the individual as the focus to the well-being of the broader Jewish community. Collective observances, rituals, celebrations and their unique relationship with God made for a uniquely robust and resilient people.
Agape (morphed as a special kind of Love) was another kettle of fish again. Agape is experienced and practiced in the context of community, but this Love also spills out of the community - extends universally beyond ourselves, family and friends - even to our enemies! Agape is Love for Love's sake. Agape Love, a self-giving, other preferring cruciform kind of Love, is uniquely Christian in the sense that the never-diminishing fountainhead of Love is in God and made manifest/demonstrated in Christ and in turn, through us.
Exploding the contextual ideas/expressions of Love, God's manifestation of Love in the flesh presents a radically different kind of Love. I wonder if Agape as an adjective (like saying divine love) is a fuller expression of Love that provides nuance and shape to an action of Love that distinguishes it from other individualistic/tribal kinds of Love. This is to say, Agape can be desire but a deeper, more whole-making, other-preferring type of desire. Agape speaks to the character qualities of the expressions of love.
God's uncontrolling Love is most certainly Pluraform. This means that it can be expressed in various ways that best fit the specific contexts, moment by moment, towards the most well-being (for all) possible.
I wonder if, over the centuries, the BIG idea of Agape has been defanged and domesticated - defined in such a narrow, dry way. This makes it very difficult for us to truly love well. For this reason, we need to recapture the radical edge of Love.
We need a thoughtful definition of Love that will guide and give shape to the way we experience and extend Love. This will shape how we move and have our being related to God, one another, ourselves and all of creation. Our definition of Love affects how we understand foundational ideas like God is Love, or Love one another as I have loved you. To this end, I like Thomas Jay Oord's definition of Love:
"To love is to act intentionally, in sympathetic response to others (including God), to promote overall well-being."
This is a pretty robust definition and goes a long way to provide structure to Love's idea (practice) to keep it from a flaccid sentiment or a rigid, narrow stoicism. At the same time, it offers significant bandwidth for greater creativity and expressions of Love that best fit the context, moment by moment.