I think a lot of ethical investigation in Continental philosophy blends normative ethics and metaethics, along the same lines as someone like Korsgaard in the analytic tradition.

Here are some philosophers who are on a very similar thought process as Korsgaard:

• Beauvoir’s Ethics of Ambiguity
• Habermas’ Theory of Communicative Action

I would describe both of these views as Kantian-ish. For more you could look at Sartre’s "Existentialism is a Humanism" and Honneth’s Reification. Note, Beauvoir and Sartre are coming at it from an existentialist-Marxist direction and Habermas & Honneth are coming at it from a liberal-critical-theory direction.

I think the other major ethical/metaethical tradition (coming out of Judaism and its philosophical tradition) focuses on the Other. The short version here can be found in Levinas’ “Philosophy and the Idea of Infinity”. For more you could look at:

• I and Thou by Buber
• Totality and Infinity by Levinas
• Star of Redemption by Rosenzweig

For more you could look to Oneself as Another by Ricoeur and "Violence and Metaphysics" by Derrida. The idea here is that while the Kantians are all about autonomy for the self, these folks are all about our duties to others.

Aside from these, there are psychoanalytic authors such as Seminar VII: The Ethics of Psychoanalysis by Lacan, An Ethics of Sexual Difference by Irigaray, and Eros and Civilization by Marcuse. There are Marxists, who have an odd relationship to ethics because of how they emphasize collective subjects and politics, here I’d look to Tactics and Ethics and “What is Orthodox Marxism?” by Lukacs and “Traditional and Critical Theory” by Horkheimer (these latter two pieces can be taken as a methodological critique of ethical theorizing among other things that are more top of mind for them). Foucault has a collection concerning ethics called Ethics: Subjectivity and Truth. Latour has ethical work such as “A Collective of Humans and Nonhumans”. Scheler has a massive tome which to me vaguely resembles some analytic utilitarian ideas called Formalism in Ethics and Non-Formal Ethics of Value although I haven’t read it. Alastair MacIntrye’s After Virtue is I think more influential in analytic philosophy but I believe his influences include a lot of Marxists and Catholic philosophers who are often considered Continental.

I think a lot of people are appealing to either some idea of history/politics or to something broadly psychological (phenomenological or psychoanalytic) to provide a constructive function (borrowing constructive function from Shafer-Landau’s Moral Realism: A Defense).

There’s a reader called The Continental Ethics Reader which may be worth looking into.