Every Classicist needs to have a grounding in its salient disciplines though. Unfortunately we do still occasionally get people who, say, only do 100% lang and lit with no real experience in linguistics, archaeology, history etc but these are becoming rarer and rarer outside of Oxford because its just a retarded way of doing things and modern scholarship kind of reflects this.
Look at any of the, many, recent commentaries you get, for example. I'm reading something on Pindar that, outside of commenting on the text, amply brings in archaeology, religion (anthropology), historical context and old fashioned philology. Because that's what is needed nowadays unless you're in a very lucky position where you can faff around writing about the poets use of the second person and psychoanalysis.
Logical really. Who is going to listen to someone on a text when they don't even know wtf was happening in the authors time, for example? Its unthinkable in other disciplines and its been permissible in ours for far too long.
Your best bet is to ask some of the first years we have, like Sappho, for example. They're covered a wide range of things already.