Holders St Benildus College go into their home tie against Clonkeen College in great form following their win at Holy Family Rathcoole in the last round.
Fellow Leinster heavyweights Clonkeen dispatched St Aiden's College in the last round but will have to stop free-scoring Benildus if they are to progress.
Another side with ominous momentum behind them is St Declan's College, who beat Colaiste Choilm 9-3 in the last 16.
Riversdale CC are up next after beating Blanchardstown rivals Hartstown CS, while the clash of Tallaght CS and Marist College, Athlone is a fascinating one.
Tallaght have squeezed through the last two rounds by a single goal -- most notably at Lucan's Colaiste Phadraig in the last 16 -- while Marist have scored 10 goals in two blistering wins.
Colaiste Ris Dundalk versus Gorey CS completes the line-up, with Gorey beating Patrician SS and the Dundalk school seeing off Drogheda's St Joseph's.
quarter-final draw: Colaiste Ris Dundalk v Gorey CS; Tallaght CS. v Marist College, Athlone; St Benildus College v Clonkeen College; Riversdale CC Blanchardstown V St Declan's College, Cabra.