In Fate, can a Master summon an Extra Class Servant during a Holy Grail War, or under any circumstances?
If I remember correctly, in the Fate/Zero and Fate/Stay Night universes, Avenger Angra Mainyu was summoned by the Einzbern in the third Holy Grail War instead of a Berserker. This would imply that it is technically possible to summon an Extra Class Servant during a standard Holy Grail War following the Fuyuki formula.