Then Paul takes on some of that narrative and says "this may be taken allegorically". He's zoomed out to look at a story arc from Abraham and his two sons through to the church situation in the first century (and today).
Alarm bells sound over breasts that represent the two testaments of the Bible and little foxes who represent sexual temptations - depending on which way you're over-reading The Song of Songs. Permit allegory and you let people make a text mean whatever they want... perhaps a Scripture-writing apostle can do it, but we better not. What's going on?
The fear of allegorical readings is that it feels like a license to print money, to make anything say anything without controls and understanding or explanation. Sometimes its heart-warming, sometimes it feels loopy. Yet using this method Paul draws out liberating gospel teaching from a narrative that we might otherwise neglect. And if he can do it there, why not elsewhere too?
Seems that all Paul does is Biblical Theology. He sees types and shadows of the gospel and finds The System of Things. Always centred upon Jesus. He's doing what the writer to the Hebrews does in showing that The Tabernacle is about The Cross. Good allegory is just that, Biblical Theology, its Typology... which for what its worth is actually what I think happens when you say The Song of Songs is about Christ and the church. Things that are models of other things... like David to Jesus... like the Tabernacle to the Cross.
Allegory like Paul does in Galatians 4 is just about stepping back and seeing the gospel, it takes a spiritual sense, a lively heart, to see the gospel where it's not explicit and yet where it's clearly painted, as it is all across the canvas of Genesis, the Pentateuch, and the whole Old and New Testaments. Failure to see how the books of Moses testify about Christ left the Pharisees unable to come to Christ when he stood in front of them. See him.