Is there a way to require a generic type to be a data class in Kotlin?

I have the feeling that what you actually want is that T should be able to copy itself with a new ID, and have an ID. Not necessarily that it is a data class. So you could just use an interface to define that.

For example:

interface CopyableWithId<out T> where T: CopyableWithId<T> {
    fun copy(newId: Long): T
    val id: Long
}

data class BarBaz(override var id: Long, var name: String): CopyableWithId<BarBaz> {
    override fun copy(newId: Long): BarBaz = copy(id = newId)
}

class Repository<T> where T : CopyableWithId<T>{

    val map: MutableMap<Long, CopyableWithId<T>> = HashMap()

    fun add(obj: T) {
        val copy = obj.copy(generateID())
        map.put(copy.id, copy)
    }

    private fun generateID(): Long {
        return 1L
    }
}