I don't think I've read much McDowell but I have read Foot and Hursthouse.. I would say Heidegger would be very useful in this context. He wasn't interested in ethics, but his idea of our shared background practices making possible our understanding of foreground phenomena e.g. the virtues or beings, seems very similar to the point that Foot and Hursthouse are making. From memory the latter two are wanting to ground the so-called objectivity of the virtues and vices in a kind of naturalism. This naturalism is basically how our species gets things done as a natural species.

I think there could be space for a radical Heideggeran interpretation of the virtues as grounded in our shared background practices rather than a "naturalism". The shared background practices aren't at all natural. The virtues could thus receive a kind of "objectivity" this way perhaps..

Hey Sophie, welcome. To be objective is to possess a type of consciousness, and as a moral agent you are directing the subjective and applying or exercising it to an external world. In Aristotle' poetics, the subject contains characteristics imitative of the ugly or beautiful, the immoral or virtuous as the aesthetic itself is this will toward moral value. A moral agent is defined as one that epitomises these virtues that imitates virtue itself. In his ethics, he outlines this imitation as a type of habitual regularity where we decisively or consciously apply a normative mimesis, but not everything, which you should know from McDowell. For instance, like goodness or love where one cannot really define the properties that make goodness or love as there are a variety. But does goodness comes before virtue? Virtue seems to explain the difference between right and wrong in terms of motivations.

I recommend The fragility of goodness by Nussbaum, personally. Good luck and feel free to throw in questions anytime as there are some who know much more than I do on VE (Y)